A108162 Least even pseudoprime > p to base p, where p = prime(n).

161038, 286, 124, 16806, 70, 244, 1228, 906, 154, 52, 66, 66, 344, 526974, 506, 286, 946, 130, 154, 370, 276, 2626, 1558, 19126, 176, 190, 946, 742, 186, 176, 3486, 190, 148, 246, 412, 10930, 186, 186, 3818, 14444, 1246, 316, 286, 276, 532, 426, 310, 246

Offset: 1

Author

Alexander Adamchuk, May 26 2007

Keywords

• nonn

Comments

Some numbers appear as a multiple terms in a(n). For example, a(n) = 946 for n = {17,27,64,66,73,75,97,113,114,117,128,139,143,152,153,155} for corresponding prime p = {59,103,311,317,367,379,509,617,619,643,719,797,823,881,883,907}. There are some twin terms such that a(n) = a(n+1). For example, a(11) = a(12) = 66, a(37) = a(38) = 186, a(113) = a(114) = 946, a(152) = a(153) = 946, a(227) = a(228) = 2626.

The indices of records are 1, 14, 354, 549, 1302, 2679, 3743, 3998, 4627, 6880, ... with record values of 161038, 526974, 1234806, 1893126, 1930546, 3347398, 3860962, 5073706, 6376126, 61161946, ... - Amiram Eldar, Sep 10 2019

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Fermat Pseudoprime.
• Index entries for sequences related to pseudoprimes

Crossrefs

Cf. A006935 (Even pseudoprimes (or primes) to base 2: n divides 2^n - 2, n even).

Cf. A130433, A090082, A130434, A090084, A130435, A130436, A130437, A130438, A130439, A130440, A130441, A130442, A130443.

Programs

Mathematica

a[n_] := Module[{p = Prime[n]}, k = p+1; If[OddQ[k], k++]; While[GCD[p, k] != 1 || PowerMod[p, k, k] != p, k+=2]; k]; Array[a, 100] (* Amiram Eldar, Sep 10 2019 *)