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A092218 Primes that divide some Euler number.

%I A092218 #11 Feb 16 2025 08:32:52
%S A092218 5,13,17,19,29,31,37,41,43,47,53,61,67,71,73,79,89,97,101,109,113,137,
%T A092218 139,149,157,173,181,193,197,223,229,233,241,251,257,263,269,277,281,
%U A092218 293,307,311,313,317,337,349,353,359,373,379,389,397,401,409,419,421
%N A092218 Primes that divide some Euler number.
%C A092218 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.
%C A092218 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
%H A092218 T. D. Noe, <a href="/A092218/b092218.txt">Table of n, a(n) for n = 1..586</a>
%H A092218 L. Carlitz, <a href="http://dx.doi.org/10.1090/S0002-9939-1954-0061124-6">Note on irregular primes</a>, Proc. Amer. Math. Soc. 5 (1954), 329-331
%H A092218 S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/bernoulli/full.pdf">Prime divisors of the Bernoulli and Euler numbers</a>
%H A092218 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EulerNumber.html">Euler Number</a>
%t A092218 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&]]
%Y A092218 Cf. A000364 (Euler numbers), A092217 (primes that do not divide any Euler number), A092219.
%K A092218 nonn
%O A092218 1,1
%A A092218 _T. D. Noe_, Feb 25 2004