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A267858 Positions of entries of A002972 that are congruent to 1 modulo 4. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 7 14:16 EST 2023. Contains 360123 sequences. (Running on oeis4.)