cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A339532 Numbers b > 1 such that the smallest three primes, i.e., 2, 3 and 5 are base-b Wieferich primes.

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%I A339532 #10 Aug 18 2025 15:44:27
%S A339532 449,557,593,649,701,757,793,901,1349,1457,1493,1549,1601,1657,1693,
%T A339532 1801,2249,2357,2393,2449,2501,2557,2593,2701,3149,3257,3293,3349,
%U A339532 3401,3457,3493,3601,4049,4157,4193,4249,4301,4357,4393,4501,4949,5057,5093,5149,5201
%N A339532 Numbers b > 1 such that the smallest three primes, i.e., 2, 3 and 5 are base-b Wieferich primes.
%F A339532 Conjectures from _Chai Wah Wu_, Aug 18 2025: (Start)
%F A339532 a(n) = a(n-1) + a(n-8) - a(n-9) for n > 9.
%F A339532 G.f.: x*(-x^8 + 108*x^7 + 36*x^6 + 56*x^5 + 52*x^4 + 56*x^3 + 36*x^2 + 108*x + 449)/(x^9 - x^8 - x + 1). (End)
%t A339532 Select[Range[2, 5250], Function[b, AllTrue[{2, 3, 5}, PowerMod[b, (# - 1), #^2] == 1 &]]] (* _Michael De Vlieger_, Dec 10 2020 *)
%o A339532 (PARI) is(n) = forprime(p=1, 5, if(Mod(n, p^2)^(p-1)!=1, return(0))); 1
%Y A339532 Cf. A256236. Row 1 of A319060.
%Y A339532 Cf. smallest k primes are base-b Wieferich primes: A339531 (k=2), A339533 (k=4), A339534 (k=5), A339535 (k=6), A339536 (k=7), A339537 (k=8).
%K A339532 nonn
%O A339532 1,1
%A A339532 _Felix Fröhlich_, Dec 08 2020