A085999 For p = prime(n), a(n) is the smallest base-2 pseudoprime N (that is, 2^(N-1) = 1 mod N) such that p divides N.

561, 645, 1729, 341, 1105, 561, 1387, 2047, 2465, 341, 2701, 6601, 645, 4371, 8321, 13747, 29341, 8911, 19951, 1387, 30889, 88561, 2047, 18721, 60701, 31621, 680627, 4033, 3277, 1905, 357761, 74665, 1419607, 88357, 4681, 8321, 422659, 83333

Offset

2,1

Comments

Tables compiled by Pinch were used. Sequence A086000 lists a(n) / prime(n).

Links

Amiram Eldar, Table of n, a(n) for n = 2..10001

R. G. E. Pinch, Pseudoprimes and their factors (FTP).

Eric Weisstein's World of Mathematics, Pseudoprime.

Example

a(11) = 341 because prime(11) = 31 and 341 is the first pseudoprime divisible by 31.

Mathematica

Table[p=Prime[n]; m=MultiplicativeOrder[4, p]; k=1; While[psp=p(1+2*m*k); PowerMod[2, psp-1, psp]!=1, k++ ]; psp, {n, 2, 100}]

Crossrefs

Cf. A001567 (base-2 pseudoprimes), A086000.

Sequence in context: A306487 A074380 A215672 * A224695 A137198 A194231

Adjacent sequences: A085996 A085997 A085998 * A086000 A086001 A086002

Keyword

easy,nonn

Author

T. D. Noe, Jul 08 2003

Status

approved