A392975 - A contribution to the On-Line Encyclopedia of Integer Sequences (OEIS)

 

(Image: Michael De Vlieger)

I recently proposed a new sequence for the On-Line Encyclopedia of Integer Sequences (OEIS). 

A Sisyphus sequence: a(0) = 0, a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest unused positive integer having the same greatest prime factor as the sum of the previous terms.

Sisyphus is a figure in Greek mythology, known as the cunning King of Corinth who was punished by Zeus to eternally roll a massive boulder up a hill in Tartarus, only for it to roll back down each time. Numerical sequences are sometimes called Sisyphus sequences when their terms climb and climb, but then drop repeatedly. 

The image above shows this process for this sequence for the first 10^6 terms. Below is a graph for how the sequence begins (first 300 terms):

One interesting feature of the sequence is the low points all appear to be prime. They begin:  7, 13, 17, 19, 23, 29, 59, 107, 137, 173, 257, 293, 467, 503...

This trend continues for at least the first 200,000 terms of the sequence.

Another feature of the sequence is that beginning with the third term, the common greatest prime factor repeats in runs of 3 or more. These factors begin:  3, 3, 3, 7, 7, 7, 7, 13, 13, 13, 13... and this trend continues for at least the first 200,000 terms of the sequence.

The proposed sequence is currently in draft form in the OEIS: https://oeis.org/draft/A392975.

(Image: Sisyphus (1548–49) by Titian, Prado Museum, Madrid, Spain)

Volumes in Higher Dimensions

(Image: Freepik)

A prior post of this blog, Atomic Interstitial Sizes in Higher Dimensions, explored how the size of gaps between tightly packed spheres changes as one moves from two-dimensional to three-dimensional and on to higher dimensions.

Grant Sanderson, host of the 3Blue1Brown YouTube channel (I highly recommend following this channel), gave an exceptional lecture explaining how to calculate the volume of high-dimensional spheres. That lecture is: https://www.youtube.com/watch?v=fsLh-NYhOoU&t=3467s. While he doesn't directly speak about the interstitial sizes of the gaps found in my post, he does approach the problem by looking at the ratio of the sphere to cube volume in higher dimensions. 

Summary of Exoplanets Discovered in 2025

An artist's illustration of the various exoplanets found, with rows of colorful planets of all colors and sizes over a dark background (Image credit: NASA's Goddard Space Flight Center)

Space.com wrote a summary of exoplanets discovered in 2025. The first exoplanet was discovered in 1995, and the number now exceeds 6000. With the James Webb Space Telescope (JWST) and other modern telescopes, this total is likely to grow by the thousands in the next few years.

One of the more interesting planets is 2M1510(AB)b which has an orbit perpendicular to the plane of the orbits of its binary stars: https://cdn.jwplayer.com/previews/WXbSE5GI.

Prior posts on JWST:

Number of planets in the universe:

https://jamesmacmath.blogspot.com/2022/01/number-of-planets-in-universe.html

Earliest star formation:

https://jamesmacmath.blogspot.com/2025/05/jwst-detects-earliest-formed-galaxies.html

Top ten JWST photographs:

https://jamesmacmath.blogspot.com/2024/07/top-ten-photographs-of-james-webb.html