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

%I A108162 #15 Feb 16 2025 08:32:58
%S A108162 161038,286,124,16806,70,244,1228,906,154,52,66,66,344,526974,506,286,
%T A108162 946,130,154,370,276,2626,1558,19126,176,190,946,742,186,176,3486,190,
%U A108162 148,246,412,10930,186,186,3818,14444,1246,316,286,276,532,426,310,246
%N A108162 Least even pseudoprime > p to base p, where p = prime(n).
%C A108162 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 A108162 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 A108162 Amiram Eldar, <a href="/A108162/b108162.txt">Table of n, a(n) for n = 1..10000</a>
%H A108162 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FermatPseudoprime.html">Fermat Pseudoprime</a>.
%H A108162 <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>
%t A108162 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 A108162 Cf. A006935 (Even pseudoprimes (or primes) to base 2: n divides 2^n - 2, n even).
%Y A108162 Cf. A130433, A090082, A130434, A090084, A130435, A130436, A130437, A130438, A130439, A130440, A130441, A130442, A130443.
%K A108162 nonn
%O A108162 1,1
%A A108162 _Alexander Adamchuk_, May 26 2007