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A105018
Indices of the irregular primes.
2
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
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
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Mar 31 2005
STATUS
approved