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A091888 Irregularity index of prime(n): number of numbers k, 1<=k<=(p-3)/2, such that p = prime(n) divides the numerator of the Bernoulli number B(2k). 2
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 2, 0, 0, 3, 0, 0, 0, 0, 1, 1, 2, 1, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,36

COMMENTS

Note offset is 2: only odd primes are considered.

LINKS

Table of n, a(n) for n=2..106.

FORMULA

0 if p is a regular prime; > 0 if p is an irregular prime

MATHEMATICA

irregPrimeIndex[n_] := Block[{p = Prime[n], cnt = 0, k = 1}, While[ 2k + 2 < p, If[ Mod[ Numerator[ BernoulliB[ 2k]], p] == 0, cnt++]; k++]; cnt]; Array[ irregPrimeIndex, 105, 2] (* Robert G. Wilson v, Sep 20 2012 *)

PROG

(PARI) a(n)=sum(i=1, (n-1)/2, if(numerator(bernfrac(2*i))%n, 0, 1))

CROSSREFS

Cf. A073277 (primes having irregularity index 2), A060975 (primes having irregularity index 3), A061576 (least prime having irregularity index n), A091887 (irregularity index of irregular prime A000928(n)).

Cf. A027641/A027642, A000367/A002445, A000928.

Sequence in context: A005926 A089803 A089811 * A083928 A074038 A204843

Adjacent sequences:  A091885 A091886 A091887 * A091889 A091890 A091891

KEYWORD

nonn

AUTHOR

T. D. Noe and Benoit Cloitre, Feb 09 2004

STATUS

approved

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Last modified November 21 13:53 EST 2017. Contains 295001 sequences.