A092218 Primes that divide some Euler number.

5, 13, 17, 19, 29, 31, 37, 41, 43, 47, 53, 61, 67, 71, 73, 79, 89, 97, 101, 109, 113, 137, 139, 149, 157, 173, 181, 193, 197, 223, 229, 233, 241, 251, 257, 263, 269, 277, 281, 293, 307, 311, 313, 317, 337, 349, 353, 359, 373, 379, 389, 397, 401, 409, 419, 421

Offset

1,1

Comments

For a prime p in this sequence, p will divide an Euler number E(k) for k < p. The density of these primes is approximately 0.66.

This sequence is the union of A002144 (primes of the form 4k+1) and A120115. Note that if prime p=1 (mod 4), then p divides E(p-1). - T. D. Noe, Jun 09 2006

Links

T. D. Noe, Table of n, a(n) for n = 1..586

L. Carlitz, Note on irregular primes, Proc. Amer. Math. Soc. 5 (1954), 329-331

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}]; t=Table[p=Prime[n]; cnt=0; Do[If[Mod[ee[[i]], p]==0, cnt++ ], {i, p}]; cnt, {n, PrimePi[500]}]; Prime[Select[Range[Length[t]], t[[ # ]]>0&]]

Crossrefs

Cf. A000364 (Euler numbers), A092217 (primes that do not divide any Euler number), A092219.

Sequence in context: A282747 A088908 A327638 * A049092 A103666 A082700

Adjacent sequences: A092215 A092216 A092217 * A092219 A092220 A092221

Keyword

nonn

Author

T. D. Noe, Feb 25 2004

Status

approved