A247208 Common bases of 1093 and 3511 as generalized Wieferich primes.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 429327, 524288, 858654, 1048576, 1717308, 2097152, 3434616, 4194304, 6869232, 8388608, 13738464, 14583415, 16777216, 27476928, 29166830, 31995179, 33554432, 46455089, 54953856, 57420033, 58333660, 58473815

Offset: 1

Author

Max Alekseyev, Nov 25 2014

Keywords

• nonn

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

• Wikipedia, Wieferich prime.

Crossrefs

Cf. A001220.

Programs

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])

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.