cp's OEIS Frontend

A211458 The irregular triangle of all bases b for which A181780(n) is a Fermat pseudoprime.

%I A211458 #10 Nov 01 2012 16:39:11
%S A211458 4,11,8,13,7,18,9,25,10,23,6,29,14,25,8,17,19,26,28,37,18,19,30,31,16,
%T A211458 35,9,29,21,34,20,37,8,55,8,12,14,18,21,27,31,34,38,44,47,51,53,57,25,
%U A211458 31,37,49,22,47,11,51,26,49,45,49,34,43,4,13,16,18,21,33
%N A211458 The irregular triangle of all bases b for which A181780(n) is a Fermat pseudoprime.
%C A211458 That is, all b for which b^(s-1) = 1 (mod s), where s is in A181780. Looking at the graph, it is apparent when a number such as 561 is a Carmichael number: there are 318 bases coprime to 561. These start at a(1937) and continue to a(2254).
%H A211458 T. D. Noe, <a href="/A211458/b211458.txt">Rows n = 1..500 of an irregular triangle</a>
%H A211458 Karsten Meyer, <a href="http://de.wikibooks.org/wiki/Pseudoprimzahlen:_Tabelle_Pseudoprimzahlen_%2815_-_4999%29">Tabelle Pseudoprimzahlen (15-4999)</a>
%e A211458 The irregular triangle begins
%e A211458 4, 11
%e A211458 8, 13
%e A211458 7, 18
%e A211458 9, 25
%e A211458 10, 23
%e A211458 6, 29
%e A211458 14, 25
%e A211458 8, 17, 19, 26, 28, 37
%e A211458 18, 19, 30, 31
%e A211458 16, 35
%t A211458 t = {}; n = 1; While[Length[t] < 100, n++; If[! PrimeQ[n], s = Select[Range[2, n-2], PowerMod[#, n-1, n] == 1 &]; If[s != {}, AppendTo[t, {n, Length[s], s}]]]]; Transpose[t][[3]]
%Y A211458 Cf. A002997 (Carmichael numbers), A181780, A211455, A211456, A211457.
%K A211458 nonn,tabf
%O A211458 1,1
%A A211458 _T. D. Noe_, Apr 13 2012