0,1

If A=[A031710] 256*n.^2+n (n>0, 257, 1026, 2307,. ,.,); Y=[A010871] 32 (32, 32, 32,..,); X=[A076338] 512*n+1 (n>0, 513, 1025, 1537, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 513^2-257 *32^2=1; 1025^2-1026*32^2=1; 1537^2-2307*32^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 11 2009]

If A=[A158420] 1024*n.^2-2*n (n>0, 1022, 4092, 9210,.,); Y=[A010871] 32 (32, 32, 32,.,); X=[A158421] 1024*n-1 (n>0, 1023, 2047, 3071, .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 1023^2-1022*32^2=1; 2047^2-4092*32^2=1; 3071^2-9210*32^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 18 2009]

Tanya Khovanova, Recursive Sequences

Cf. A031710, A076338 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 11 2009]

Cf. A158420, A158421 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 18 2009]

Sequence in context: A022988 A023474 A126271 this_sequence A022366 A165853 A035037

Adjacent sequences: A010868 A010869 A010870 this_sequence A010872 A010873 A010874

nonn

N. J. A. Sloane (njas(AT)research.att.com).