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Search: id:A092217
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| A092217 |
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Primes that do not divide any Euler number. |
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+0
4
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..264
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, 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]]]
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CROSSREFS
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Cf. A000364 (Euler numbers), A092218 (primes that divide some Euler number), A092219.
Sequence in context: A039787 A129940 A128631 this_sequence A007481 A121268 A101173
Adjacent sequences: A092214 A092215 A092216 this_sequence A092218 A092219 A092220
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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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