The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A298212

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A298212

Smallest n such that A060645(a(n)) = 0 (mod n), i.e., x=A023039(a(n)) and y=A060645(a(n)) is the fundamental solution of the Pell equation x^2 - 5*(n*y)^2 = 1.
(history; published version)

#25 by Alois P. Heinz at Thu May 11 18:34:57 EDT 2023

STATUS

proposed

approved

#24 by Robert C. Lyons at Thu May 11 18:30:56 EDT 2023

STATUS

editing

proposed

#23 by Robert C. Lyons at Thu May 11 18:09:43 EDT 2023

PROG

(Python:)

.... n = n+1

.... y1, y0, i = 0, yf, 1

.... while y0%n != 0:

........ y1, y0, i = y0, x*y0-y1, i+1

.... print(n, i)

STATUS

approved

editing

#22 by Joerg Arndt at Sat Nov 16 10:52:07 EST 2019

STATUS

reviewed

approved

#21 by Joerg Arndt at Sat Nov 16 04:11:30 EST 2019

STATUS

proposed

reviewed

#20 by Jean-François Alcover at Sat Nov 16 03:51:25 EST 2019

STATUS

editing

proposed

#19 by Jean-François Alcover at Sat Nov 16 03:51:22 EST 2019

MATHEMATICA

b[n_] := b[n] = Switch[n, 0, 0, 1, 4, _, 18 b[n - 1] - b[n - 2]];

a[n_] := For[k = 1, True, k++, If[Mod[b[k], n] == 0, Return[k]]];

a /@ Range[100] (* Jean-François Alcover, Nov 16 2019 *)

STATUS

approved

editing

#18 by N. J. A. Sloane at Mon Jan 22 18:44:41 EST 2018

STATUS

proposed

approved

#17 by Jon E. Schoenfield at Tue Jan 16 08:04:29 EST 2018

STATUS

editing

proposed

#16 by Jon E. Schoenfield at Tue Jan 16 08:04:26 EST 2018

NAME

Smallest n such that A060645(a(n)) = 0 (mod n), i.e. , x=A023039(a(n)) and y=A060645(a(n)) is the fundamental solution of the Pell equation x^2 - 5*(n*y)^2 = 1.

STATUS

proposed

editing