A105018 Indices of the irregular primes.

12, 17, 19, 26, 27, 32, 35, 37, 51, 55, 56, 58, 61, 62, 63, 64, 69, 71, 75, 77, 79, 80, 82, 84, 89, 90, 91, 94, 99, 100, 101, 102, 106, 107, 108, 111, 112, 113, 114, 115, 118, 119, 120, 122, 123, 124, 125, 129, 133, 134, 135, 137, 139, 140, 141, 142, 144, 146, 151

Offset

1,1

References

Carl Ludwig Siegel, Zu zwei Bemerkungen Kummers, Nachrichten der Akademie der Wissenschaften in Göttingen, 1964, pp. 51-57.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Irregular Prime.

Formula

Conjecture (Siegel, 1964): Limit_{n -> oo} a(n)/n = 1 - 1 / sqrt(e) (A290506). Of the 788060 primes < 12000000, 310443 are irregular.

A000040(a(n)) = A000928(n). - Amiram Eldar, Mar 06 2019

Mathematica

fQ[n_] := Block[{ p = Prime[ n ], k = 1}, While[ 2k <= p - 3 && Mod[ Numerator[ BernoulliB[ 2k]], p] != 0, k++ ]; If[ 2k != p - 1, True, False]]; Select[ Range[2, 151], fQ[ # ] &]

Crossrefs

Cf. A000040, A000928, A105019, A290506.

Sequence in context: A350686 A064825 A162918 * A154488 A336890 A302359

Adjacent sequences: A105015 A105016 A105017 * A105019 A105020 A105021

Keyword

nonn

Author

Robert G. Wilson v, Mar 31 2005

Status

approved