A267858 Positions of entries of A002972 that are congruent to 1 modulo 4.

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, 43, 45, 47, 49, 50, 52, 53, 55, 56, 57, 59, 60, 63, 65, 66, 68, 69, 72, 73, 74, 77, 78, 85, 87, 88, 89, 90, 91, 93, 94, 95, 96, 100, 104, 105, 106, 108, 110, 112, 115, 119, 120, 122, 127, 128, 131

Offset

1,2

Comments

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.

If a positive integer m is not in this sequence then A002972(m) == 3 (mod 4).

Links

Table of n, a(n) for n=1..71.

Formula

A002972(a(n)) == 1 (mod 4), n >= 1.

Example

n=1: A002972(1) = 1 == 1 (mod 4). But because m = 2 is not in this sequence A002972(2) = 3 == 3 (mod 4).

Mathematica

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 *)

Crossrefs

Cf. A002145, A002972.

Sequence in context: A121502 A180644 A202110 * A108943 A194081 A288041

Adjacent sequences: A267855 A267856 A267857 * A267859 A267860 A267861

Keyword

nonn

Author

Wolfdieter Lang, Feb 06 2016

Status

approved