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

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, 35, 9, 29, 21, 34, 20, 37, 8, 55, 8, 12, 14, 18, 21, 27, 31, 34, 38, 44, 47, 51, 53, 57, 25, 31, 37, 49, 22, 47, 11, 51, 26, 49, 45, 49, 34, 43, 4, 13, 16, 18, 21, 33

Offset: 1

Author

T. D. Noe, Apr 13 2012

Keywords

• nonn
• tabf

Comments

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).

Examples

			The irregular triangle begins
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, 35
		

Links

• T. D. Noe, Rows n = 1..500 of an irregular triangle
• Karsten Meyer, Tabelle Pseudoprimzahlen (15-4999)

Crossrefs

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

Programs

Mathematica

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]]