A211458 - OEIS

%I #10 Nov 01 2012 16:39:11

%S 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 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 31,37,49,22,47,11,51,26,49,45,49,34,43,4,13,16,18,21,33

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

%C 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 T. D. Noe, <a href="/A211458/b211458.txt">Rows n = 1..500 of an irregular triangle</a>

%H Karsten Meyer, <a href="http://de.wikibooks.org/wiki/Pseudoprimzahlen:_Tabelle_Pseudoprimzahlen_%2815_-_4999%29">Tabelle Pseudoprimzahlen (15-4999)</a>

%e The irregular triangle begins

%e 4, 11

%e 8, 13

%e 7, 18

%e 9, 25

%e 10, 23

%e 6, 29

%e 14, 25

%e 8, 17, 19, 26, 28, 37

%e 18, 19, 30, 31

%e 16, 35

%t 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 Cf. A002997 (Carmichael numbers), A181780, A211455, A211456, A211457.

%K nonn,tabf

%O 1,1

%A _T. D. Noe_, Apr 13 2012