A229855 a(n) = 384*n + 257.

257, 641, 1025, 1409, 1793, 2177, 2561, 2945, 3329, 3713, 4097, 4481, 4865, 5249, 5633, 6017, 6401, 6785, 7169, 7553, 7937, 8321, 8705, 9089, 9473, 9857, 10241, 10625, 11009, 11393, 11777, 12161, 12545, 12929, 13313, 13697, 14081, 14465, 14849, 15233, 15617, 16001

Offset: 0

Author

Arkadiusz Wesolowski, Oct 01 2013

Keywords

• nonn
• easy

Comments

Every composite Fermat number has at least two divisors of the form 384*n + 257, n > 0.

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 0..1000
• Wikipedia, Fermat number.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A000215, A016789, A094358, A229853, A229854, A229856.

Programs

Magma

[384*n+257 : n in [0..40]];

Maple

seq(384*n+257, n=0..40);

Mathematica

Table[384*n + 257, {n, 0, 40}]

PARI

for(n=0, 40, print1(384*n+257, ", "));

Formula

G.f.: (257 + 127*x)/(1 - x)^2.

a(n) = 128*A016789(n) + 1.

From Elmo R. Oliveira, Dec 08 2024: (Start)

E.g.f.: exp(x)*(257 + 384*x).

a(n) = 2*a(n-1) - a(n-2) for n > 1. (End)