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Sequence and first differences together list all positive numbers exactly once

EXAMPLE Sequence reads 1 3 7 12 18 26 35 45..., differences are 2 4 5, 6, 8, 9, 10 ... and the point is that every number not in the sequence itself appears among the differences. This property (together with the fact that both the sequence and the sequence of first differences are increasing) defines the sequence!

How to Slow Down Your Biological Clock

Death is inevitable. But the journey getting there is far from universal. The average life expectancy at birth worldwide is now around 73 years but varies widely between countries and even between individual states in America. I, and presumably many readers, know some people who have barely lost a step as they’ve gotten older, as well as people who sharply declined as they entered their golden years. These realities invite the question: How can we significantly slow down our biological clock? A

Indie App Spotlight: ‘Coffee in the Sun’ helps you find an ideal outdoor spot to hang

Welcome to Indie App Spotlight. This is a weekly 9to5Mac series where we showcase the latest apps in the indie app world. If you’re a developer and would like your app featured, get in contact. If you’re trying to find an ideal spot outdoors, whether that be a coffee shop, bar, or restaurant – but want to know whether or not it’ll be in the sun or shade, Coffee in the Sun is the premier app for you. It’s a vibe coded app, but it certainly works well – and the developer put an adequate amount of

Topics: app coffee ll shade sun

Stop Wasting Money: 20 Pointless Kitchen Gadgets Chefs Warn Against

We all know how important preserving valuable kitchen space is. There's simply no room for single-function gadgets that are barely used, or worse, don't do much of anything at all. If you can't stand clutter -- and wasting money -- avoiding overrated and useless tools is a good place to start. To find out which kitchen tools aren't worth the space they occupy, I turned to five professional chefs. These career cooks are the ultimate authority on which kitchen gadgets should get the boot -- espec

The 24 Best Movies on Amazon Prime Right Now (July 2025)

In Recent years, Netflix and Apple TV+ have been duking it out to have the most prestigious film offerings, but some of the best movies are on Amazon Prime Video. The streamer was one of the first to go around picking up film festival darlings and other lovable favorites, and they’re all still there in the library, so if they flew under your radar the first time, now is the perfect time to catch up. Our picks for the best movies on Amazon Prime are below. All the films in our guide are included

Breville Luxe Brewer Review (2025): Good Drip, Real Cold Brew

The new Breville Luxe Brewer is designed for hot coffee. It makes excellent, subtle, hot drip coffee. But it also does something that almost no other fancy coffee maker on the market achieves. It makes real cold brew coffee—the sweet and gentle stuff, the cool elixir of smooth summers and milky heaven. The Luxe is part of a new generation of drip coffee makers that has helped transform drip coffee from bitter office fuel into a subject for connoisseurship. The Luxe's predecessor, the Precision

Rubin Observatory’s Stunning Result Proves It’s a ‘Game Changer’ for Spotting Dangerous Asteroids

Astronomers usually keep their eyes on the sky, but on Monday, June 23, the community turned its attention toward Washington, D.C., as scientists from the Vera C. Rubin Observatory unveiled the telescope’s first images. Many have waited more than 20 years to see Rubin in action, and its initial findings did not disappoint. Rubin, a joint initiative of the National Science Foundation (NSF) and the Department of Energy’s (DOE) Office of Science, recently conducted its first 10 hours of test obser

Anker issues new global recall for five power bank models over fire hazard

Just days after issuing a voluntary recall for the Anker PowerCore 10000, the company has now issued a second, broader recall, this time with global reach and five additional power bank models affected. Anker says the move is a proactive step following recent improvements to its internal quality assurance systems. While the company claims the risk of malfunction is low, it’s recalling the affected models “out of an abundance of caution.” All five power banks flagged in the recall use lithium-io

How vulnerable is critical infrastructure to cyberattack in the US?

is a senior science reporter covering energy and the environment with more than a decade of experience. She is also the host of Hell or High Water: When Disaster Hits Home , a podcast from Vox Media and Audible Originals. Our water, health, and energy systems are increasingly vulnerable to cyberattack. Now, when tensions escalate — like when the US bombed nuclear facilities in Iran this month — the safety of these systems becomes of paramount concern. If conflict erupts, we can expect it to be

The inference trap: How cloud providers are eating your AI margins

This article is part of VentureBeat’s special issue, “The Real Cost of AI: Performance, Efficiency and ROI at Scale.” Read more from this special issue. AI has become the holy grail of modern companies. Whether it’s customer service or something as niche as pipeline maintenance, organizations in every domain are now implementing AI technologies — from foundation models to VLAs — to make things more efficient. The goal is straightforward: automate tasks to deliver outcomes more efficiently and s

How runtime attacks turn profitable AI into budget black holes

This article is part of VentureBeat’s special issue, “The Real Cost of AI: Performance, Efficiency and ROI at Scale.” Read more from this special issue. AI’s promise is undeniable, but so are its blindsiding security costs at the inference layer. New attacks targeting AI’s operational side are quietly inflating budgets, jeopardizing regulatory compliance and eroding customer trust, all of which threaten the return on investment (ROI) and total cost of ownership of enterprise AI deployments. AI

TikTok is testing its own version of Instagram’s ‘broadcast channels’

TikTok is testing a new messaging tool called “bulletin boards,” the social network confirmed to TechCrunch on Friday. The feature lets brands and creators share public, one-to-many messages to their followers. Bulletin boards are pretty similar to Instagram’s broadcast channels feature that launched in 2023. Just like with broadcast channels on Instagram, only the creator of a bulletin board can post messages, and followers are limited to leaving emoji reactions. Bulletin boards support text,

A New Threads Feature Saves You From Seeing and Posting Spoilers: Here's How It Works

Social media can accidentally spoil a streaming movie or show for those who haven't yet watched it. Threads, the popular social media platform from Meta, now has a new feature that could save you from spoiling your next watch. The new feature allows users to mark media and text posts as spoilers. If it's a photo, the spoiler will then appear blurred in feeds, and text will be grayed out. Clicking on both types makes the spoiler visible. Netflix and Marvel are the first major studios to use the

Eufy’s Omni C20 mopping robovac is $300 off for a limited time

After a long week, the last thing I want to do is clean my floors (they’re seriously overdue for a cleaning). Busting out the vacuum and mopping can be tiring. That’s why I’m a big fan of robot vacuums, especially ones with built-in mops that can handle all the cleaning on their own. Speaking of, you can pick up the Eufy Robot Vacuum Omni C20 at Amazon and Eufy for $399.98 ($300 off), matching its all-time low. This deal may be around for just a matter of hours. The Omni C20 is one of Eufy’s ne

How your Pixel phone can now help you shoot expert-level photos and video

Max Buondonno/ZDNET For a lot of people, camera quality is a huge selling point when picking a cellphone. Having so many different options can be overwhelming, though. So, how do you ensure that you're getting the most out of your phone's capabilities? A new Google Pixel Camera mode wants to teach you everything you need to know. Also: The best camera phones: Tested by experts When Google announced its 2025 Pixel Feature Drop, one feature went relatively unnoticed -- something called "Camer

Hertz turns to AI for rental car inspections, faces backlash over fees

A hot potato: Hertz is ushering in a new era of vehicle inspections by deploying artificial intelligence-powered scanners at select locations across the US. The move is intended to improve the accuracy and transparency of the rental car damage inspection process. However, for some customers, the technology has led to new frustrations and unexpected costs. The company's new system, developed in partnership with Israeli firm UVeye, is already operational at major hubs such as Hartsfield-Jackson A

Topics: ai damage fee hertz new

Google will show you more news from your favorite sources - here's how to set it up

SOPA Images / Contributor / Getty Thanks to a new Google Labs feature, you can now tell Google which news sources you want to see more often in Top Stories (as long as you opt in). The company detailed the feature in a blog post Thursday, as part of six ways you can better personalize your Search experience. With the "Preferred Sources" experiment in Labs, you might choose to see world or political news from your preferred outlet, news about your favorite sports team from the newspaper beat re

Transmitting data via ultrasound without any special equipment

There are secret messages flying all around you all the time, being transmitted via, most of the time, electromagnetic waves going from antenna to antenna. ELOs “Secret Messages” is a song about posting conspiracy theories via WiFi. But what if you need to get a few bytes from device A to device B (one of the hard problems in computer science!) and you don’t feel like making sure they’re both connected to the same network? Well, fortunately, another channel is available to us - sound, or for a

Delivery message alerts could be coming to Now Brief (APK teardown)

Joe Maring / Android Authority TL;DR Now Brief may soon alert you about package deliveries. The feature will remind you how many messages you received about deliveries for that day. Since debuting on One UI 7, Samsung has continued to flesh out the Now Brief feature. Earlier today, we reported that Samsung is working on adding info cards for parking spot reminders, smart home alerts, and wearable battery warnings. Now we have found that it could gain another pretty useful type of alert. Auth

The 1975 at Glastonbury 2024: Livestream Their Headline Festival Set From Anywhere for Free

After a nine-year absence from Worthy Farm, The 1975 are back at Glastonbury, with the band this time playing a prestigious headline set on the festival's Pyramid main stage. Below, we'll outline which live TV streaming service will be streaming this headline act at Glastonbury, wherever you are in the world. We'll also explain how to use a VPN if you're outside of the UK. Led by provocative frontman Matty Healy, The 1975 last played the event as an early act on the festival's Other Stage back

Mortgage Rate Predictions: Will Military Conflict, Tariffs and the Fed Keep Rates High?

Buyers should keep an eye on the possibility of rate cuts in the next few months. Tharon Green/CNET The housing market is hardly immune to political and economic volatility, yet mortgage rates have been eerily calm over the last period. Since the spring, the average rate for a 30-year fixed mortgage has moved in a mostly narrow range around 6.8% and 7%. Mortgage rates were expected to gradually improve in 2025. However, the Trump administration's inflationary tariffs, deficit spending and geop

AI overviews and an AI chatbot are coming to YouTube. Here's what they look like

NurPhoto / Contributor/Getty The next time you search for something on YouTube, you might notice some differences, thanks to two new AI-powered tools. Also: The top 20 AI tools of 2025 - and the #1 thing to remember when you use them The streaming video platform is rolling out a new way to display search results. While not officially related, the feature is pretty similar to Google's AI Overviews. YouTube gave an example in a short video showcasing the feature. If you search for something li

Show HN: A Python Language Server, Mypy-compatible

In 2012, I created Jedi—a Python auto-completion library that eventually reached millions of users and billions of downloads. But as the ecosystem evolved, one limitation became clear: speed. Jedi’s architecture couldn’t deliver the performance needed for large-scale projects. In 2020, I started over—with everything I’d learned—building ZubanLS from the ground up in Rust. After five years of full-time work, ZubanLS is now the first truly fast Python language server. ZubanLS is built for profes

These 7 Automatic Cat Feeders Were the Best We Tested (2025)

Another We Tested Photograph: Molly Higgins Oneisall Cordless WiFi Automatic Cat Feeder for $60: I had high hopes for this cordless feeder that boasts a rechargeable battery with a 100-day life and an integrated app, but it's just too unreliable. Through the app, you can program up to 10 daily meals (in 1-12 portions each), monitor pets' eating habits, and customize meal calls. Unlike other apps, you're not able to choose portion size, but instead have to multiply the number of servings. The a

We’re learning more about what weight-loss drugs do to the body

We know they can suppress appetite, lower blood sugar, and lead to dramatic weight loss. We also know that they come with side effects, which can include nausea, diarrhea, and vomiting. But we are still learning about some of their other effects. On the one hand, these seemingly miraculous drugs appear to improve health in other ways, helping to protect against heart failure, kidney disease, and potentially even substance-use disorders, neurodegenerative diseases, and cancer. But on the other,

Is Google readying a rival to iOS’ Contact Poster? (APK teardown)

Apple TL;DR We’ve spotted clues that indicate Google is working on a “calling card” feature for Android. The feature may allow for full-screen images and custom fonts for incoming calls. Speculatively, it could be similar to iOS’ Contact Posters, enabling users to personalize their call display. Google and Apple frequently look at each other’s operating systems for inspiration on what next to bring to their own. We’ve seen iOS copy features like widgets, free app icon placement on the home s

Why I recommend this Bluetooth speaker for outdoor listening (and it's not a Bose)

ZDNET's key takeaways The LG Xboom Bounce is available for $199. It offers big bass, intuitive smart lighting features, and its durability makes it great for both indoor and outdoor use. Although it has some home speaker features, it might be too rugged-looking for an indoor speaker. View now at Best Buy The weather is getting warmer, which means it's imperative to have a Bluetooth speaker on hand for cookouts, days by the pool, or any of your indoor and outdoor summer gatherings. Over the la

Gemini in Google Sheets now lets you type a prompt to tell it exactly what to do

Jaque Silva/NurPhoto /Getty If you use Google Sheets for work, Gemini is about to make your life a lot easier. Also: Google's new free AI agent brings Gemini right to your command line - here's how to try it Sheets already has the capability for Gemini to assist with creating tables and formulas, generating graphs and charts, and handling tasks like conditional formatting, sorting, and filtering. Now you can enter a prompt in a cell to tell Gemini what you want to do. Also: Google Earth jus

Google starts rolling out Pixel Camera ‘education hub’ to help you master every feature

Ryan Haines / Android Authority TL;DR Google has started rolling out the education hub in the Pixel Camera app. The feature was announced in the June Pixel Drop. It allows users to learn how to use various Pixel Camera features and is rolling out on version 9.9 of the Pixel Camera app for the Pixel 6 and above. Google has begun rolling out the new “education hub” in its Pixel Camera app. Available in version 9.9 of the app for Pixel 6 and newer devices, this feature was first introduced in t

Hawaiian Airlines discloses cyberattack, flights not affected

Hawaiian Airlines, the tenth-largest commercial airline in the United States, is investigating a cyberattack that has disrupted access to some of its systems. With over 7,000 employees, 235 average daily flights, and a fleet of over 60 airplanes, Hawaiian Airlines connects Hawai'i with 15 U.S. mainland cities and 10 other destinations across Asia and the Pacific. The airline stated in a statement issued on Thursday morning that the incident didn't affect flight safety and has already contacted