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A247208
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Common bases of 1093 and 3511 as generalized Wieferich primes.
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3
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..41.
Wikipedia, Wieferich prime.
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FORMULA
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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) + 4726582775529.
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PROG
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(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])
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CROSSREFS
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Cf. A001220
Sequence in context: A220493 A118655 A249169 * A011782 A034008 A123344
Adjacent sequences: A247205 A247206 A247207 * A247209 A247210 A247211
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KEYWORD
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nonn
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AUTHOR
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Max Alekseyev, Nov 25 2014
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STATUS
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approved
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