This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A267859 #25 Sep 12 2016 07:46:21
%S A267859 2,-6,2,10,2,10,-14,10,-6,10,18,2,-6,-14,-22,-14,-22,26,18,-14,2,-30,
%T A267859 26,-30,2,26,18,10,34,26,-22,18,10,34,-14,34,-38,2,-6,-30,34,-14,42,
%U A267859 -38,10,-22,42,-38,26,2,-46,10,34,-38,50,26,50,-46,2,10,-30,-54,18,-38,50,34,-22,10,50,-54
%N A267859 The p-defect p - N(p) of the elliptic curve y^2 = x^3 + x for primes p congruent to 1 modulo 4 (A002144).
%C A267859 See A002172 for a differently signed sequence.
%C A267859 The number N(p) of solutions modulo a prime p of the elliptic curve y^2 = x^3 + x (of discriminant -4) is given for all p in A095978.
%C A267859 The p-defect a_p = p - N(p) for prime 2 and primes congruent to 3 modulo 4 vanishes.
%C A267859 A002144(n) - (a(n)/2)^2 = (2*A002973(n))^2, n >= 1. See the formula for A095978 for primes 1 (mod 4).
%C A267859 This sequence gives also the non-vanishing p-defects of the elliptic curve y^2 = x^3 - 4*x. See a comment on A138515 with the Martin and Ono link for the modularity series for these two elliptic curves. - _Wolfdieter Lang_, May 26 2016
%D A267859 J. H. Silverman, A Friendly Introduction to Number Theory, 3rd ed., Pearson Education, Inc, 2006, p. 398. In the 4th ed., 2014, p. 371.
%H A267859 Seiichi Manyama, <a href="/A267859/b267859.txt">Table of n, a(n) for n = 1..1000</a>
%F A267859 a(n) = A002144(n) - A095978(m) with A002144(n) = A000040(m), n >= 1.
%F A267859 a(n) = A138515((A002144(n) - 1)/4), n >= 1. - _Wolfdieter Lang_, May 26 2016
%e A267859 n = 2: p = A002144(2) = 13 = A000040(6), m = 6, a(2) = 13 - A095978(6) = 13 - 19 = -6.
%e A267859 n = 2: -6 = A138515((A002144(2) - 1)/4) =
%e A267859 A138515(3) = -6. - _Wolfdieter Lang_, May 26 2016
%t A267859 terms = 100; A002144 = Select[Range[5, 20*terms, 4], PrimeQ]; A095978[n_] := Module[{p, xy, x}, p = Prime[n]; If[n==1 || Mod[p, 4]==3, Return[p]]; xy = {Re[#], Im[#]}& @ FactorInteger[p, GaussianIntegers -> True][[2, 1]]; x = SelectFirst[xy, OddQ]; If[Mod[x, 4]==1, p - 2*x, p + 2*x]]; a[n_] := (p = A002144[[n]]; m = PrimePi[p]; p - A095978[m]); Array[a, terms] (* _Jean-François Alcover_, Feb 26 2016, after _Robert Israel_ (A095978) *)
%Y A267859 Cf. A000040, A002144, A002172, A095978, A138515.
%K A267859 sign
%O A267859 1,1
%A A267859 _Wolfdieter Lang_, Feb 06 2016