%I #25 Dec 26 2018 04:37:30
%S 1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,
%T 131072,262144,429327,524288,858654,1048576,1717308,2097152,3434616,
%U 4194304,6869232,8388608,13738464,14583415,16777216,27476928,29166830,31995179,33554432,46455089,54953856,57420033,58333660,58473815
%N Common bases of 1093 and 3511 as generalized Wieferich primes.
%C Numbers b such that b^1092 == 1 (mod 1093^2) and b^3510 == 1 (mod 3511^2). Here 1093 and 3511 are the currently known Wieferich primes (A001220) and thus b = 2 belongs to this sequence by definition.
%C Contains the powers of 2 (A000079) as a subsequence.
%C Contains infinitely many primes, which are listed in A247214.
%C The characteristic function is multiplicative: if x,y belong to this sequence, then so does x*y. Furthermore, if p^k belongs to this sequence, then so does p. Therefore, the sequence consists of products of powers of primes from A247214.
%C Numbers b such that b^49140 == 1 (mod 1093^2*3511^2). - _Jianing Song_, Dec 26 2018
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Wieferich_prime">Wieferich prime</a>.
%F The union of 1092*3510 = 3832920 arithmetic progressions with the same difference 1093^2*3511^2 = 14726582775529. For any n, a(n+3832920) = a(n) + 14726582775529.
%o (PARI) r1=znprimroot(1093^2)^1093; r2=znprimroot(3511^2)^3511; v=vector(1092*3510); for(i=0,1091,for(j=0,3509, v[i*3510+j+1]=lift(chinese(r1^i,r2^j)) )); v=vecsort(v); vector(100,i,v[i])
%Y Cf. A001220.
%K nonn
%O 1,2
%A _Max Alekseyev_, Nov 25 2014