0,1

If A=[A156711] 144*n^2+127*n+28 (28,299,858,..,], or A=[A156719] 144*n^2-127*n+28 (28,45,350,...,), or A=[A156635] 144*n^2-n (143,574,1293), or A=[A031702] (145,578,1299,..., except the term 97994); Y=[A010863] (24,24,24,...,); X=[A156702] (127,161,287,..,) then we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 127^2-28*24^2=1; 161^2-45*24^2=1; 287^2-143*24^2=1; 289^2-145*24^2=1; 415^2-299*24^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 21 2009]

If A=[A158369] 576*n.^2+2*n (n>0, 578, 2308, 5190,.,); Y=[A010863] 24 (24, 24, 24 ,.,); X=[A158370] 576*n+1 (n>0, 577, 1153, 1729, .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 577^2-578*24^2=1; 1153^2-2308*24^2=1; 1729^2-5190*24^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 17 2009]

If A=[A158371] 576*n.^2-2*n (n>0, 574, 2300, 5178,.,); Y=[A010863] 24 (24, 24, 24 ,.,); X=[A158372] 576*n-1 (n>0, 575, 1151, 1727, .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 575^2-574*24^2=1; 1151^2-2300*24^2=1; 1727^2-5178*24^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 17 2009]

Tanya Khovanova, Recursive Sequences

Vincenzo Librandi, X^2-AY^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 21 2009]

A156711, A156702, A156711, A156719, A156635, A031702 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 21 2009]

Cf. A158369, A158370 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 17 2009]

Cf. A158371, A158372 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 17 2009]

Sequence in context: A128560 A022980 A023466 this_sequence A115028 A099543 A040553

Adjacent sequences: A010860 A010861 A010862 this_sequence A010864 A010865 A010866

nonn

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