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

Author

Altug Alkan, Mar 17 2016

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A000129, A048739, A270342.

Programs

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), ", ")));