A092217 Primes that do not divide any Euler number.

2, 3, 7, 11, 23, 59, 83, 103, 107, 127, 131, 151, 163, 167, 179, 191, 199, 211, 227, 239, 271, 283, 331, 347, 367, 383, 431, 439, 443, 467, 479, 487, 499, 503, 523, 547, 599, 607, 631, 643, 647, 659, 683, 719, 727, 743, 787, 823, 827, 839, 859, 863, 883, 911

Offset

1,1

Comments

After computing the Euler numbers, finding the non-divisors is simple because the Euler numbers satisfy a Kummer congruence. See Wagstaff for details. The density of these primes is approximately 0.33.

Links

Amiram Eldar, Table of n, a(n) for n = 1..500 (terms 1..264 from T. D. Noe)

Samuel S. Wagstaff, Jr., Prime divisors of the Bernoulli and Euler numbers, in: Number Theory for the Millennium III, A K Peters, 2002, pp. 357-374.

Eric Weisstein's World of Mathematics, Euler Number

Mathematica

ee=Table[Abs[EulerE[2i]], {i, 1000}]; t=Table[p=Prime[n]; cnt=0; Do[If[Mod[ee[[i]], p]==0, cnt++ ], {i, p}]; cnt, {n, PrimePi[1000]}]; Prime[Flatten[Position[t, 0]]]

Crossrefs

Cf. A000364 (Euler numbers), A092218 (primes that divide some Euler number), A092219.

Sequence in context: A227199 A129940 A128631 * A191659 A007481 A238312

Adjacent sequences: A092214 A092215 A092216 * A092218 A092219 A092220

Keyword

nonn

Author

T. D. Noe, Feb 25 2004

Status

approved