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

Author

T. D. Noe, Feb 25 2004

Keywords

• nonn

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

Crossrefs

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

Programs

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&]]