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Search: id:A092218
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| A092218 |
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Primes that divide some Euler number. |
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+0
5
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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 (noe(AT)sspectra.com), Jun 09 2006
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..586
S. S. Wagstaff, Jr., Prime divisors of the Bernoulli and Euler numbers
Eric Weisstein's World of Mathematics, Euler Number
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MATHEMATICA
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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&]]
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CROSSREFS
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Cf. A000364 (Euler numbers), A092217 (primes that do not divide any Euler number), A092219.
Sequence in context: A067696 A050598 A088908 this_sequence A049092 A103666 A082700
Adjacent sequences: A092215 A092216 A092217 this_sequence A092219 A092220 A092221
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Feb 25 2004
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