The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A298210

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A298210

Smallest n such that A001542(a(n)) == 0 (mod n), i.e., x=A001541(a(n)) and y=A001542(a(n)) is the fundamental solution of the Pell equation x^2 - 2*(n*y)^2 = 1.
(history; published version)

#37 by Alois P. Heinz at Thu May 11 18:14:19 EDT 2023

STATUS

proposed

approved

#36 by Robert C. Lyons at Thu May 11 18:07:14 EDT 2023

STATUS

editing

proposed

#35 by Robert C. Lyons at Thu May 11 18:07:12 EDT 2023

PROG

(Python:)

xf, yf = 3, 2

x, n = 2*xf, 0

.... 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

#34 by Michel Marcus at Sat Nov 16 03:23:17 EST 2019

STATUS

reviewed

approved

#33 by Joerg Arndt at Sat Nov 16 03:08:07 EST 2019

STATUS

proposed

reviewed

#32 by Jean-François Alcover at Sat Nov 16 03:01:06 EST 2019

STATUS

editing

proposed

#31 by Jean-François Alcover at Sat Nov 16 03:01:01 EST 2019

MATHEMATICA

b[n_] := b[n] = Switch[n, 0, 0, 1, 2, _, 6 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

#30 by N. J. A. Sloane at Sat Jan 27 13:42:22 EST 2018

STATUS

proposed

approved

#29 by Jon E. Schoenfield at Wed Jan 24 01:18:41 EST 2018

STATUS

editing

proposed

#28 by Jon E. Schoenfield at Wed Jan 24 01:18:22 EST 2018

COMMENTS

If n is save a safe prime (i.e., in A005385) and n in {7,23} (mod 24) then (n - Legendre symbol (n/2)) / a(n) = 2, i.e., a(n) is a Sophie Germain prime (A005384).