|
%I #9 Feb 26 2016 05:00:26
%S 1,3,4,5,6,8,10,11,12,18,19,21,23,25,26,27,28,29,30,32,33,34,36,38,41,
%T 43,45,47,49,50,52,53,55,56,57,59,60,63,65,66,68,69,72,73,74,77,78,85,
%U 87,88,89,90,91,93,94,95,96,100,104,105,106,108,110,112,115,119,120,122,127,128,131
%N Positions of entries of A002972 that are congruent to 1 modulo 4.
%C This sequence is needed for the number of solutions modulo primes congruent to 1 modulo 4 of the elliptic curve y^2 = x^3 + x See A095978.
%C If a positive integer m is not in this sequence then A002972(m) == 3 (mod 4).
%F A002972(a(n)) == 1 (mod 4), n >= 1.
%e n=1: A002972(1) = 1 == 1 (mod 4). But because m = 2 is not in this sequence A002972(2) = 3 == 3 (mod 4).
%t pmax = 2000; odd[p_] := Module[{k, m}, 2m+1 /. ToRules[Reduce[k>0 && m >= 0 && (2k)^2 + (2m+1)^2 == p, {k, m}, Integers]]]; Reap[For[n=1; p=5, p < pmax, p = NextPrime[p], If[Mod[p, 4]==1, If[Mod[odd[p], 4]==1, Sow[n]]; n++]]][[2, 1]] (* _Jean-François Alcover_, Feb 26 2016 *)
%Y Cf. A002145, A002972.
%K nonn
%O 1,2
%A _Wolfdieter Lang_, Feb 06 2016
|
