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

1,1

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).

Links

T. D. Noe, Rows n = 1..500 of an irregular triangle

Karsten Meyer, Tabelle Pseudoprimzahlen (15-4999)

Example

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

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]]

Crossrefs

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

Sequence in context: A354274 A205136 A096735 * A222284 A330683 A020949

Adjacent sequences: A211455 A211456 A211457 * A211459 A211460 A211461

Keyword

nonn,tabf

Author

T. D. Noe, Apr 13 2012

Status

approved