A105018 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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