The On-Line Encyclopedia of Integer Sequences (OEIS)

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Smallest nonnegative value taken on by 5x^2 - ny^2 for an infinite number of integer pairs (x, y).
(history; published version)

#9 by Bruno Berselli at Mon Oct 10 02:45:46 EDT 2016

STATUS

proposed

approved

#8 by Jean-François Alcover at Mon Oct 10 02:31:45 EDT 2016

STATUS

editing

proposed

#7 by Jean-François Alcover at Mon Oct 10 02:31:21 EDT 2016

MATHEMATICA

Table[TimeConstrained[a[n], 300], {n, 1, 105}] (* _Jean-François Alcover_, Oct 10 2016 *)

STATUS

proposed

editing

Discussion

Mon Oct 10

02:31

Jean-François Alcover: Once again! (merci)

#6 by Jean-François Alcover at Mon Oct 10 02:13:21 EDT 2016

STATUS

editing

proposed

Discussion

Mon Oct 10

02:23

Michel Marcus: Forgot to sign

#5 by Jean-François Alcover at Mon Oct 10 02:12:49 EDT 2016

MATHEMATICA

f[n_, z_] := FindInstance[x > 0 && y > 0 && 5*x^2 - n*y^2 == z, {x, y}, Integers, 1]; a[n_] := For[z = 0, z <= 5, z = z + GCD[n, 5], fz = f[n, z]; If[fz =!= {}, Print["a(", n, ") = ", z, " {x, y} = ", {x, y} /. fz[[1]]]; Return[z]]];

a[49] := (Print["a(49) = ", 5, " {x, y} = ", {51841, 16560}]; 5);

a[81] := (Print["a(81) = ", 5, " {x, y} = ", {161, 40}]; 5);

a[83] := (Print["a(83) = ", 5, " {x, y} = ", {1919, 471}]; 5);

a[98] := (Print["a(98) = ", 3, " {x, y} = ", {31, 7}]; 3);

Table[TimeConstrained[a[n], 300], {n, 1, 105}]

STATUS

approved

editing

#4 by Russ Cox at Fri Mar 30 18:35:39 EDT 2012

AUTHOR

_David W. Wilson (davidwwilson(AT)comcast.net)_

Discussion

Fri Mar 30

18:35

OEIS Server: https://oeis.org/edit/global/202

#3 by N. J. A. Sloane at Sat Sep 13 03:00:00 EDT 2003

KEYWORD

nonn,new

nonn

AUTHOR

David W. Wilson (davidwwilson(AT)attbicomcast.comnet)

#2 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

KEYWORD

nonn,new

nonn

AUTHOR

dww

David W. Wilson (davidwwilson(AT)attbi.com)

#1 by N. J. A. Sloane at Sat Dec 11 03:00:00 EST 1999

NAME

Smallest nonnegative value taken on by 5x^2 - ny^2 for an infinite number of integer pairs (x, y).

DATA

1, 2, 2, 1, 0, 5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 4, 3, 2, 1, 0, 5, 5, 5, 5, 5, 5, 2, 5, 5, 5, 1, 5, 3, 5, 5, 5, 5, 5, 5, 5, 1, 3, 2, 1, 0, 5, 5, 5, 5, 5, 5, 5, 3, 5, 5, 5, 5, 5, 1, 5, 1, 2, 5, 5, 5, 5, 2, 5, 5, 5, 1, 5, 5, 5, 5, 4, 3, 2, 1, 0, 5, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 5, 1, 5, 5, 5, 5

OFFSET

1,2

KEYWORD

nonn

AUTHOR

dww

STATUS

approved