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A089020 First value y satisfying x^2 - 3*y^2 = d^2, where d=A072330(n). 8
1, 4, 3, 7, 5, 8, 11, 16, 20, 7, 13, 20, 12, 44, 9, 51, 17, 52, 57, 55, 19, 11, 16, 28, 72, 91, 36, 65, 69, 13, 23, 68, 20, 25, 105, 15, 88, 76, 44, 120, 145, 40, 87, 119, 29, 85, 24, 17, 155, 132, 93, 31, 44, 104, 52, 92, 95, 19, 140, 200, 28, 105, 231, 35, 100, 185, 105, 120 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Jean-François Alcover, Table of n, a(n) for n = 1..1000

MATHEMATICA

terms = 1000;

nmax = 12 terms;

okQ[n_] := AllTrue[FactorInteger[n][[All, 1]], MatchQ[Mod[#, 12], 1|11]&];

A072330 = Select[Range[nmax], okQ];

a[n_] := Module[{a, b, c, d, p}, d = If[n <= Length[A072330], A072330[[n]], Print["nmax = ", nmax, " insufficient"]; Exit[]]; If[n == 1, 1, For[b = 2 d, True, b++, a = b - d; c = b + d; p = (a + b + c)/2; If[IntegerQ[p] && IntegerQ[Sqrt[p (p - a) (p - b) (p - c)]] && GCD[a, b, c] == 1, Return[ Sqrt[b^2 - 4 d^2]/(2 Sqrt[3])]]]]];

a /@ Range[terms] (* Jean-François Alcover, Mar 07 2020 *)

CROSSREFS

For corresponding x see A089019.

Cf. A072330, A072360, A086909, A089019, A096672, A096673, A096674.

Sequence in context: A276760 A257876 A093051 * A046560 A131413 A205392

Adjacent sequences:  A089017 A089018 A089019 * A089021 A089022 A089023

KEYWORD

nonn

AUTHOR

Lekraj Beedassy, Nov 04 2003

EXTENSIONS

Extended by Ray Chandler, Jul 03 2004

STATUS

approved

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Last modified March 31 19:37 EDT 2020. Contains 333151 sequences. (Running on oeis4.)