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A308243 Index of E-irregularity of prime(n). 1
0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 3, 1, 0, 1, 2, 2, 1, 1, 0, 1, 0, 3, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,59

COMMENTS

A prime p >= 5 is an E-irregular prime if there is an even integer 2*k such that 2 <= 2*k <= p-3 and p divides E(2*k), where E(i) is the i-th Euler number (A000364). The pair (p, 2*k) is called an E-irregular pair. The number of such pairs for a given p is called the index of E-irregularity of p (cf. Ernvall, Metsänkylä, 1978, p. 618).

In other words, a prime p is E-irregular if its index of E-irregularity is > 0, which is the case if p is a term of A092218. Otherwise, p is E-regular and is a term of A092217.

LINKS

Table of n, a(n) for n=1..87.

R. Ernvall and T. Metsänkylä, Cyclotomic invariants and E-irregular primes, Mathematics of Computation 32 (1978), 617-629.

PROG

(PARI) a000364(n) = subst(bernpol(2*n+1), 'x, 1/4)*4^(2*n+1)*(-1)^(n+1)/(2*n+1) \\ after Charles R Greathouse IV in A000364

a(n) = my(p=prime(n), e=2, i=0); while(e <= p-3, if(a000364(e)%p==0, i++); e=e+2); i

CROSSREFS

Cf. A000364, A092217, A092218, A120337.

Sequence in context: A031253 A291624 A291635 * A268386 A122779 A120323

Adjacent sequences:  A308240 A308241 A308242 * A308244 A308245 A308246

KEYWORD

nonn

AUTHOR

Felix Fröhlich, May 16 2019

STATUS

approved

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Last modified October 21 07:32 EDT 2021. Contains 348148 sequences. (Running on oeis4.)