Accidental Desultory Cogitations

Random thoughts on a variety of topics, but mostly on science and technology.

Saturday, March 7, 2026

A characterization of OEIS A393797

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 In OEIS sequence A393336 , the $n$-th term is the sum of positions of 1's minus sum of positions of 0's in the binary expansion of ...
Thursday, July 31, 2025

Binomial coefficients modulo m

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I have recently written a Python function to compute binomial coefficients modulo m where m is a positive integer. It uses Lucas' theo...
Monday, July 7, 2025

Sum of rows of Pascal's triangle modulo 8

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 Pascal's triangle modulo $m$ can present interesting numerical structures. For instance, for $m=2$, the resulting triangle is the fract...
Saturday, April 5, 2025

Oblong pandigital numbers

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In this blogpost , I wrote about pandigital numbers (numbers in base n>1 that uses the numbers 0 to n-1 exactly once) that are also squar...

Nearest integer with the same Hamming weight

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Theorem: For a positive integer n, the nearest integer not equal to n with the same Hamming weight as n is larger than n if and only if n is...
Thursday, February 29, 2024

Happy Leap Day 2024 and a modest proposal of determining leap years.

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Today is February 29, 2024, a leap day. It occurs once during leap years once every 4 years when the year is divisible by 4, with some excep...
Monday, February 26, 2024

Python module implementing various classes of graphs for networkx

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  I have recently uploaded a python module to pypi : graph-generators : Python functions to compute various classes of networkx graphs. Ava...

Square pandigital numbers

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Let a pandigital number in base $n$ be defined as a number that uses the digits from $0$ to $n-1$ exactly once. See OEIS sequence A050278 f...
Sunday, August 7, 2022

Songs with a single rhyme

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I was listening to some Mandarin Chinese songs and noticed that the song  "絲路" (Silk Road) by  梁靜茹 ( Fish Leong) and the song  陪我...
Friday, July 22, 2022

Happy π approximation day 2022!

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Today is π approximation day (also known as casual π day). I talked about this 2 years ago in this blog post . I first learned about the app...
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