A108162 - OEIS

%I #15 Feb 16 2025 08:32:58

%S 161038,286,124,16806,70,244,1228,906,154,52,66,66,344,526974,506,286,

%T 946,130,154,370,276,2626,1558,19126,176,190,946,742,186,176,3486,190,

%U 148,246,412,10930,186,186,3818,14444,1246,316,286,276,532,426,310,246

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

%C 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.

%C 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

%H Amiram Eldar, <a href="/A108162/b108162.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FermatPseudoprime.html">Fermat Pseudoprime</a>.

%H <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>

%t 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 *)

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

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

%K nonn

%O 1,1

%A _Alexander Adamchuk_, May 26 2007