A229853 a(n) = 384*n + 1.

1, 385, 769, 1153, 1537, 1921, 2305, 2689, 3073, 3457, 3841, 4225, 4609, 4993, 5377, 5761, 6145, 6529, 6913, 7297, 7681, 8065, 8449, 8833, 9217, 9601, 9985, 10369, 10753, 11137, 11521, 11905, 12289, 12673, 13057, 13441, 13825, 14209, 14593, 14977, 15361, 15745

Offset: 0

Author

Arkadiusz Wesolowski, Oct 01 2013

Keywords

• nonn
• easy

Comments

Every composite Fermat number has a divisor of the form 384*n + 1, 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, A094358, A229854, A229855, A229856.

Programs

Magma

[384*n+1 : n in [0..40]];

Maple

seq(384*n+1, n=0..40);

Mathematica

Table[384*n + 1, {n, 0, 40}]

PARI

for(n=0, 40, print1(384*n+1, ", "));

Formula

G.f.: (1 + 383*x)/(1 - x)^2.

From Elmo R. Oliveira, Apr 04 2025: (Start)

E.g.f.: exp(x)*(1 + 384*x).

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