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 A092219 Least even k such that the Euler number E(k) is divisible by prime(n), or 0 if there is no k. 3

%I

%S 0,0,4,0,0,12,16,10,0,28,22,36,40,12,14,52,0,6,26,28,72,18,0,88,96,62,

%T 0,0,108,112,0,0,42,128,146,0,156,0,0,172,0,180,0,74,196,0,0,132,0,

%U 228,232,0,210,126,256,212,268,0,8,280,0,292,90,86,312,316,0,336,0,18,70

%N Least even k such that the Euler number E(k) is divisible by prime(n), or 0 if there is no k.

%C A prime p will either divide an Euler number E(k) for k < p or divide no Euler number. This sequence can be used to find A092218, primes that divide Euler numbers and A092217, primes that divide no Euler number.

%H T. D. Noe, <a href="/A092219/b092219.txt">Table of n, a(n) for n = 1..850</a>

%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EulerNumber.html">Euler Number</a>

%t ee=Table[Abs[EulerE[2i]], {i, 500}]; Table[p=Prime[n]; i=1; While[i<=p && Mod[ee[[i]], p]>0, i++ ]; If[i>p, 0, 2i], {n, PrimePi[500]}]

%Y Cf. A000364 (Euler numbers).

%K nonn

%O 1,3

%A _T. D. Noe_, Feb 25 2004

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Last modified October 23 16:53 EDT 2018. Contains 316529 sequences. (Running on oeis4.)