0,2

Also 11*x^2+1 is a square. n=11 in PARI script below. - Cino Hilliard (hillcino368(AT)gmail.com), Mar 08 2003

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

H. Brocard, Notes e'le'mentaires sur le proble`me de Peel, Nouvelles Correspondance Math\'{e}matique, 4 (1878), 161-169.

"Questions D'Arithmetique", Question 3686, Solution by H.L. Mennessier, Mathesis, 65(4, Supplement) 1956, pp. 1-12.

Index entries for sequences related to linear recurrences with constant coefficients

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

Tanya Khovanova, Recursive Sequences

Lim a(n)/a(n-1) = 10 + 3*Sqrt(11); for all n in the sequence, 11*n^2 + 1 is a perfect square. - Gregory V. Richardson (omomom(AT)hotmail.com), Oct 06 2002

a(n) = [(10+3*Sqrt(11))^n - (10-3*Sqrt(11))^n] / (2*Sqrt(11)) - Gregory V. Richardson (omomom(AT)hotmail.com), Oct 06 2002

a(n) = 19*(a(n-1)+a(n-2))-a(n-3). a(n) = 21*(a(n-1)-a(n-2))+a(n-3). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Sep 20 2006

A001084:=3*z/(1-20*z+z**2); [Conjectured by S. Plouffe in his 1992 dissertation.]

(PARI) nxsqp1(m, n) = { for(x=1, m, y = n*x*x+1; if(issquare(y), print1(x" ")) ) }

Equals 3 * A075843.

Sequence in context: A144659 A115490 A065889 this_sequence A137150 A081854 A085990

Adjacent sequences: A001081 A001082 A001083 this_sequence A001085 A001086 A001087

nonn,easy

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

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 19 2000