0,1

If A=[A156810] (70,44,468,1342,..,], or A=[A156812](44,70,546,1472,...,), or A=[A156813] (224,898,2022,..,), or A=[A156814] (226,902,2028,3604,..); Y=[A010869] (30,30,30,...,) and X=[A156840] (199,251,449,451,..), then we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 199^2-44*30^2=1; 251^2-70*30^2=1; 449^2-224*30^2=1; 451^2-226*30^2=1; 649^2-468*30^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]

If A=[A158406] 900*n.^2+2*n (n>0, 902, 3604, 8106,.,); Y=[A010869] 30 (30, 30, 30, ,.,); X=[A158407] 900*n+1 (n>0, 901, 1801, 2701, .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 901^2-902*30^2=1; 1801^2-3604*30^2=1; 2701^2-8106*30^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 18 2009]

If A=[A158408] 900*n.^2-2*n (n>0, 898, 3596, 8094,.,); Y=[A010869] 30 (30, 30, 30, ,.,); X=[A158409] 900*n-1 (n>0, 899, 1799, 2699, .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 899^2-898*30^2=1; 1799^2-3596*30^2=1; 2699^2-8094*30^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 18 2009]

Tanya Khovanova, Recursive Sequences

Vincenzo Librandi, X^2-AY^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]

Cf. A156810, A156812, A156813, A156814, A15840 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]

Vf. A158406, A158407 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 18 2009]

Cf. A158408, A158409 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 18 2009]

Sequence in context: A125564 A056958 A056997 this_sequence A078287 A040871 A022364

Adjacent sequences: A010866 A010867 A010868 this_sequence A010870 A010871 A010872

nonn

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