A092219 Least even k such that the Euler number E(k) is divisible by prime(n), or 0 if there is no k.

0, 0, 4, 0, 0, 12, 16, 10, 0, 28, 22, 36, 40, 12, 14, 52, 0, 6, 26, 28, 72, 18, 0, 88, 96, 62, 0, 0, 108, 112, 0, 0, 42, 128, 146, 0, 156, 0, 0, 172, 0, 180, 0, 74, 196, 0, 0, 132, 0, 228, 232, 0, 210, 126, 256, 212, 268, 0, 8, 280, 0, 292, 90, 86, 312, 316, 0, 336, 0, 18, 70

Offset

1,3

Comments

A prime p will either divide an Euler number E(k) for k < p or divide no Euler number. This sequence can be used to find A092218, primes that divide Euler numbers and A092217, primes that divide no Euler number.

Links

T. D. Noe, Table of n, a(n) for n = 1..850

S. S. Wagstaff, Jr., Prime divisors of the Bernoulli and Euler numbers

Eric Weisstein's World of Mathematics, Euler Number

Mathematica

ee=Table[Abs[EulerE[2i]], {i, 500}]; Table[p=Prime[n]; i=1; While[i<=p && Mod[ee[[i]], p]>0, i++ ]; If[i>p, 0, 2i], {n, PrimePi[500]}]

Crossrefs

Cf. A000364 (Euler numbers).

Sequence in context: A035539 A178517 A049207 * A262227 A336731 A069026

Adjacent sequences: A092216 A092217 A092218 * A092220 A092221 A092222

Keyword

nonn

Author

T. D. Noe, Feb 25 2004

Status

approved