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

Author

T. D. Noe, Feb 25 2004

Keywords

• nonn

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

Crossrefs

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

Programs

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]]]