A270449 Odd integers n such that the sum of the Pell numbers A000129(0) + ... + A000129(n-1) is divisible by n*(n+1)/2.

13, 61, 157, 181, 193, 337, 385, 397, 541, 673, 733, 769, 877, 1153, 1201, 1213, 1453, 1873, 1933, 2017, 2029, 2557, 2593, 2797, 3217, 3313, 3517, 4177, 4273, 4561, 4621, 4657, 5101, 5233, 5437, 5581, 5641, 6337, 6637, 6781, 7057, 7213, 7393, 7481, 7537, 7561, 7933, 8221, 8317

Offset

1,1

Comments

Sequence contains the prime numbers most of the time. Nonprime terms of this sequence are 385, 111361, 111841, 155041, 186961 ...

Links

Table of n, a(n) for n=1..49.

Example

13 is a term because (0 + 1 + 2 + 5 + 12 + 29 + 70 + 169 + 408 + 985 + 2378 + 5741 + 13860) / (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13) = 260.

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, 1e4, if(a048739(n-1) % ((n+1)*(n+2)/2) == 0 && (n+1) % 2 == 1, print1((n+1), ", ")));

Crossrefs

Cf. A000129, A048739, A270342.

Sequence in context: A086361 A119151 A081589 * A139880 A127876 A361657

Adjacent sequences: A270446 A270447 A270448 * A270450 A270451 A270452

Keyword

nonn

Author

Altug Alkan, Mar 17 2016

Status

approved