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.

A331021 Numbers k such that gcd(k^2, 2^(k-1) - 1) > k.

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%I A331021 #14 Jan 08 2020 03:27:56
%S A331021 1093,3511,398945,796797,1592501,1990353,2388205,3183909,3581761,
%T A331021 4377465,5173169,5968873,6165316,10345245,11538801,15119469,16313025,
%U A331021 17506581,18302285,20291545,23076509,23872213,24650731,26657177,29442141,36205625,36974341,37001329,38194885
%N A331021 Numbers k such that gcd(k^2, 2^(k-1) - 1) > k.
%C A331021 Conjecture: each term is a multiple of a Wieferich prime.
%C A331021 Prime numbers in this sequence are the Wieferich primes A001220.
%C A331021 Pseudoprime (A001567) terms are 3581761, 5173169, 5968873, 23872213, 36974341, 53711113, ...
%C A331021 The terms of A291194 that are not in this sequence are 1194649, 2786057, 3979613, 4775317, 5571021, ....
%H A331021 Giovanni Resta, <a href="/A331021/b331021.txt">Table of n, a(n) for n = 1..4184</a> (terms < 10^12)
%e A331021 1093 is a term since gcd(1093^2, 2^1092 - 1) = 1093^2 > 1093.
%t A331021 seqQ[n_] := GCD[n^2, PowerMod[2, n - 1, n^2] - 1] > n; Select[Range[10^7], seqQ]
%o A331021 (PARI) isok(n) = gcd(n^2, 2^(n-1) - 1) > n; \\ _Michel Marcus_, Jan 07 2020
%Y A331021 Cf. A001220, A001567.
%Y A331021 Subsequence of A291194.
%K A331021 nonn
%O A331021 1,1
%A A331021 _Amiram Eldar_ and _Thomas Ordowski_, Jan 07 2020