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

Author

T. D. Noe, Jul 08 2003

Keywords

• easy
• nonn

Comments

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

Examples

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

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.

Crossrefs

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

Programs

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}]