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 A120337 Euler-irregular primes p dividing E(2k) for some 2k < p-1. 9
 19, 31, 43, 47, 61, 67, 71, 79, 101, 137, 139, 149, 193, 223, 241, 251, 263, 277, 307, 311, 349, 353, 359, 373, 379, 419, 433, 461, 463, 491, 509, 541, 563, 571, 577, 587, 619, 677, 691, 709, 739, 751, 761, 769, 773, 811, 821, 877, 887, 907, 929, 941, 967, 971, 983 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..1000 Su Hu, Min-Soo Kim, A note on the irregular primes with respect to Euler polynomials, arXiv:1510.01558 [math.NT], 2015. Su Hu, Min-Soo Kim, Pieter Moree, Min Sha, Irregular primes with respect to Genocchi numbers and Artin's primitive root conjecture, arXiv:1809.08431 [math.NT], 2018. R. Mestrovic, A search for primes p such that Euler number E_{p-3} is divisible by p, arXiv preprint arXiv:1212.3602 [math.NT], 2012. - From N. J. A. Sloane, Jan 25 2013 Prime Pages, Euler Irregular Samuel S. Wagstaff, Prime divisors of the Bernoulli and Euler numbers, Number theory for the millennium, III, 2002, pp. 357-374, 2002. MR 1956285. FORMULA The (trivial) divisors of E(2n) are given by the theorem of Sylvester (1861): Let p prime with p=1 (mod 4), p-1|2n, p^k|2n then p^{k+1} | E(2n). EXAMPLE a(1) = 19 because 19 divides E(10) = -19*2659 and 10 + 1 < 19. MAPLE A120337_list := proc(bound) local ae, F, p, m, maxp; F := NULL; for m from 2 by 2 to bound do   p := nextprime(m+1);   ae := abs(euler(m));   maxp := min(ae, bound);   while p <= maxp do       if ae mod p = 0       then F := F, p fi;       p := nextprime(p);    od; od; sort([F]) end: # Peter Luschny, Apr 25 2011 MATHEMATICA fQ[p_] := Block[{k = 1}, While[ 2k +1 < p && Mod[ EulerE[ 2k], p] != 0, k++]; p > 2k +1]; Select[ Prime@ Range@ 168, fQ@# &] (* Robert G. Wilson v, Dec 10 2014 *) CROSSREFS Cf. A092218, A120115. Sequence in context: A178251 A164320 A154418 * A120115 A157995 A043298 Adjacent sequences:  A120334 A120335 A120336 * A120338 A120339 A120340 KEYWORD nonn AUTHOR Stefan Krämer, Jun 22 2006 EXTENSIONS Terms 251 through 983 from Peter Luschny, Apr 25 2011 STATUS approved

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Last modified October 14 05:08 EDT 2019. Contains 327995 sequences. (Running on oeis4.)