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%I M2115 #50 Jan 16 2018 02:37:32
%S 2,19,29,199,569,809,1289,1439,2539,3319,3559,3919,5519,9419,9539,
%T 9929,11279,11549,13229,14489,17239,18149,18959,19319,22279,24359,
%U 27529,28789,32999,33029,36559,42899,45259,46219,49529,51169,52999,55259
%N Supersingular primes of the elliptic curve X_0 (11).
%C The primes for which A006571(p) == 0 (mod p) are called supersingular for the elliptic curve "11a3" and form sequence A006962. A prime p>2 is in A006962 if and only if A006571(p) = 0. - _Michael Somos_, Dec 25 2010
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Joerg Arndt, <a href="/A006962/b006962.txt">Table of n, a(n) for n = 1..747</a> (first 60 terms from Seiichi Manyama)
%H S. Lang and H. F. Trotter, <a href="http://dx.doi.org/10.1007/BFb0082087">Frobenius Distribution in GL_2-Extensions</a> Lect Notes Math. 504, 1976, see p. 267.
%t maxPi = 500; QP = QPochhammer; s = q*(QP[q]*QP[q^11])^2 + O[q]^(Prime[ maxPi] + 1); Reap[Do[If[Mod[SeriesCoefficient[s, p], p] == 0, Print[p]; Sow[p]], {p, Prime[Range[maxPi]]}]][[2, 1]] (* _Jean-François Alcover_, Nov 29 2015, adapted from PARI *)
%o (PARI) forprime(p=2, 2999, if(polcoeff(x * sqr(eta(x + O(x^p)) * eta(x^11 + O(x^p))), p)%p == 0, print1(p","))) /* _Michael Somos_, Dec 25 2010 */
%o (PARI) \\ gp -s 30G < A006962.gp
%o { N = 10^8 + 2;
%o default(seriesprecision,N);
%o V = Vec((eta(q) * eta(q^11))^2);
%o forprime(p=2,N, if( V[p]%p == 0, print1(p,", ") ) );
%o } \\ _Joerg Arndt_, Sep 10 2016
%o (Ruby)
%o require 'prime'
%o def A006962(n)
%o ary = []
%o cnt = 1
%o Prime.each(10 ** 7){|p|
%o a = Array.new(p, 0)
%o (0..p - 1).each{|i| a[(i * i) % p] += 1}
%o s = 0
%o (0..p - 1).each{|i|
%o s += a[(i * i * i - 4 * i * i + 16) % p]
%o break if s > p
%o }
%o if p == s
%o ary << p
%o cnt += 1
%o return ary if cnt > n
%o end
%o }
%o end # _Seiichi Manyama_, Sep 10 2016
%Y Cf. A006571.
%K nonn
%O 1,1
%A _N. J. A. Sloane_
%E a(29)-a(38) from _Michael Somos_, Dec 25 2010
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