OFFSET
1,2
COMMENTS
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.
Contains the powers of 2 (A000079) as a subsequence.
Contains infinitely many primes, which are listed in A247214.
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.
Numbers b such that b^49140 == 1 (mod 1093^2*3511^2). - Jianing Song, Dec 26 2018
LINKS
Jianing Song, Table of n, a(n) for n = 1..10000
Wikipedia, Wieferich prime.
Index entries for linear recurrences with constant coefficients, order 3832921.
FORMULA
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.
G.f.: (P(x)*(1-x) + 14726582775529*x^3832921)/((1-x)*(1-x^3832920)), where P(x) = Sum_{n=1..3832920} a(n)*x^n. - Jianing Song, Jun 08 2026
PROG
(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])
CROSSREFS
KEYWORD
nonn
AUTHOR
Max Alekseyev, Nov 25 2014
STATUS
approved