login
A158404
841n + 1.
2
842, 1683, 2524, 3365, 4206, 5047, 5888, 6729, 7570, 8411, 9252, 10093, 10934, 11775, 12616, 13457, 14298, 15139, 15980, 16821, 17662, 18503, 19344, 20185, 21026, 21867, 22708, 23549, 24390, 25231, 26072, 26913, 27754, 28595, 29436
OFFSET
1,1
COMMENTS
The identity (841*n+1)^2-(841*n^2+2*n)*(29)^2=1 can be written as a(n)^2-A158403(n)*(29)^2=1.
LINKS
Vincenzo Librandi, X^2-AY^2=1
E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(29^2*t+2)).
FORMULA
G.f.: x*(842-x)/(1-x)^2.
a(n) = 2*a(n-1)-a(n-2).
MATHEMATICA
LinearRecurrence[{2, -1}, {842, 1683}, 50]
NestList[#+841&, 842, 40] (* Harvey P. Dale, Dec 14 2012 *)
PROG
(Magma) I:=[842, 1683]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 841*n + 1.
CROSSREFS
Cf. A158403.
Sequence in context: A342841 A337730 A049530 * A004929 A031736 A154473
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 18 2009
STATUS
approved