A270345 Composite integers n such that the sum of the Pell numbers A000129(0) + ... + A000129(n-1) is divisible by n.

4, 8, 16, 24, 32, 48, 64, 72, 96, 120, 128, 144, 168, 169, 192, 216, 240, 256, 264, 272, 288, 336, 360, 384, 385, 432, 480, 504, 512, 528, 544, 576, 600, 648, 672, 720, 768, 792, 816, 840, 864, 960, 961, 1008, 1024, 1056, 1080, 1088, 1105, 1121, 1152, 1176, 1200, 1296, 1320, 1344

Offset

1,1

Comments

Nonprime terms of A270342.

Terms that are not divisible by 4 are 169, 385, 961, 1105, 1121, 3827, 4901, 6265, 6441, 6601, 7107, 7801, 8119, ...

Links

Table of n, a(n) for n=1..56.

Example

4 is a term because 0 + 1 + 2 + 5 = 8 is divisible by 4.
8 is a term because 0 + 1 + 2 + 5 + 12 + 29 + 70 + 169 = 288 is divisible by 8.

Prog

(PARI) a048739(n) = local(w=quadgen(8)); -1/2+(3/4+1/2*w)*(1+w)^n+(3/4-1/2*w)*(1-w)^n;
for(n=1, 1e3, if(a048739(n-1) % (n+1) == 0 && !isprime(n+1), print1(n+1, ", ")));

Crossrefs

Cf. A000129, A048739, A270342.

Sequence in context: A306219 A160746 A160740 * A335668 A181823 A308985

Adjacent sequences: A270342 A270343 A270344 * A270346 A270347 A270348

Keyword

nonn

Author

Altug Alkan, Mar 15 2016

Status

approved