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A128363 a(n) = least k such that the remainder when 23^k is divided by k is n.

%I A128363 #24 Jul 18 2025 13:55:02
%S A128363 2,3,5,19,262,17,58,9,10,13,14,55,86,12153,514,111823,95,25,30,12147,
%T A128363 68,235,29,280517,56,27,502,16805,51,49,166,35,62,1837,38,977969,82,
%U A128363 39,1370,289,122,9822698929535,65,133,697,161,303,19445,50,147,259,1247
%N A128363 a(n) = least k such that the remainder when 23^k is divided by k is n.
%H A128363 Max Alekseyev et al., <a href="/A128363/a128363_2.txt">Table of n, a(n) for n = 1..10000 with -1 for large entries where a(n) has not yet been found</a>
%t A128363 t = Table[0, {10000} ]; k = 1; While[ k < 4000000000, a = PowerMod[23, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t (* _Robert G. Wilson v_, Aug 04 2009 *)
%t A128363 Table[Module[{k=1},While[PowerMod[23,k,k]!=n,k++];k],{n,35}] (* The program generates the first 35 terms of the sequence. *) (* _Harvey P. Dale_, Jul 18 2025 *)
%Y A128363 Cf. A128361, A128362, A128364, A128365, A128366, A128367, A128368, A128369, A129370, A128371, A128372.
%Y A128363 Cf. A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821, A128154, A128155, A128156, A128157, A128158, A128159, A128160.
%Y A128363 Cf. A128149, A128150, A128172.
%K A128363 hard,nonn
%O A128363 1,1
%A A128363 _Alexander Adamchuk_, Feb 27 2007
%E A128363 a(42), a(64) from _Hagen von Eitzen_, Aug 04 2009
%E A128363 a(750), a(770), a(234), a(274), a(406), a(600), a(610), a(754) from _Daniel Morel_, May 31, Aug 24, Sep 20 2010
%E A128363 a(84) from _Max Alekseyev_, Apr 13 2012