A158421 a(n) = 1024*n - 1.

1023, 2047, 3071, 4095, 5119, 6143, 7167, 8191, 9215, 10239, 11263, 12287, 13311, 14335, 15359, 16383, 17407, 18431, 19455, 20479, 21503, 22527, 23551, 24575, 25599, 26623, 27647, 28671, 29695, 30719, 31743, 32767, 33791, 34815, 35839

Offset: 1

Author

Vincenzo Librandi, Mar 18 2009

Keywords

• nonn
• easy

Comments

The identity (1024*n-1)^2-(1024*n^2-2*n)*(32)^2=1 can be written as a(n)^2-A158420(n)*(32)^2=1.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• 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*(32^2*t-2)).
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A158420.

Programs

Magma

I:=[1023, 2047]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

Mathematica

LinearRecurrence[{2,-1},{1023,2047},50]

PARI

a(n) = 1024*n - 1.

Formula

a(n) = 2*a(n-1)-a(n-2).

G.f.: x*(1023+x)/(1-x)^2.