To Wit: 2/2

Today is 2/2/22, so here’s a little problem about palindromes. For each set of integers <= 1[0…]1 in base 10, find the cumulative count of palindromes exactly divisible by 1, 2, 3, 4, 5, 6, 7, 8 and 9. For example, 2, 4, 6 and 8 are the 4 palindromes exactly divisible by 2 that are less than 11, so countdiv(2) = 4 for pal <= 11; 3, 6 and 9 are the 3 palindromes exactly divisible by 3, so countdiv(3) = 3; and so on:

count for palindromes <= 11 (prime)

countdiv(1) = 10
countdiv(2) = 4
countdiv(3) = 3
countdiv(4) = 2
countdiv(5) = 1
countdiv(6) = 1
countdiv(7) = 1
countdiv(8) = 1
countdiv(9) = 1


count for palindromes <= 101 (prime)

countdiv(1) = 19
countdiv(2) = 8
countdiv(3) = 6
countdiv(4) = 4
countdiv(5) = 2
countdiv(6) = 2
countdiv(7) = 2
countdiv(8) = 2
countdiv(9) = 2


count for palindromes <= 1001 = 7 * 11 * 13

countdiv(1) = 109
countdiv(2) = 48
countdiv(3) = 36
countdiv(4) = 24
countdiv(5) = 12
countdiv(6) = 15
countdiv(7) = 15
countdiv(8) = 12
countdiv(9) = 12


Some interesting patterns appear as the ceiling-palindromes reach 10001, 100001, 1000001… And one particular pattern doesn’t always disappear when you try the same problem in other bases. I hope to say more on 22/2/22.

Core War…

In terms of my core ambitions for 2022, I hope to continue the fight against such things as the reprehensible and repulsive phrase “in terms of”, the pretentious and throbbingly urgent adjective “core”, and the cheap trick of trailing dots… I know that I won’t win and that the Hive-Mind will continue to buzz deafeningly at core venues like The Guardian, The London Review of Books and The Shropshire Advertiser, but so what? In the core words of Samuel in terms of Johnson:

[I]t remains that we retard what we cannot repel, that we palliate what we cannot cure. Life may be lengthened by care, though death cannot be ultimately defeated: tongues, like governments, have a natural tendency to degeneration; we have long preserved our constitution, let us make some struggles for our language. — Samuel Johnson, Preface to a Dictionary of the English Language (1755)


Elsewhere Other-Accessible

Ex-term-in-ate! — core interrogation of why “in terms of” is so despicable, deplorable and downright disgusting…
Don’t Do Dot — core interrogation of why “…” is so despicable, deplorable and downright disgusting dot dot dot


Post-Performative Post-Scriptum

How should the first line of this incendiary intervention begin? I suggest: “In terms of my core ambitions for 2022…” → “Among my main ambitions…”