A263549 Numbers k such that k divides the sum of the first k primes with odd indices.

1, 3, 67, 141, 2201, 2625, 8153, 10187, 11089, 136515, 138377, 1543419, 1712109, 5097739, 51562297, 1459124841, 42825210689

Offset: 1

Author

Altug Alkan, Oct 21 2015

Keywords

• nonn
• more

Comments

a(n) is always an odd number since the first prime is 2.

How do a(n) and A263546(n) compare asymptotically?

Examples

			1 is in the sequence because prime(1) = 2 is divisible by 1.
3 is in the sequence because prime(1) + prime(3) + prime(5) = 2 + 5 + 11 = 18 is divisible by 3.
		

Crossrefs

Cf. A045345, A077131, A263541, A263546.

Programs

Mathematica

Select[Range@ 10000, Divisible[Sum[Prime[2 i - 1], {i, 1, #}], #] &] (* Michael De Vlieger, Oct 21 2015 *)

PARI

list(lim)=my(v=List(), k, s, t); forprime(p=2, , if((t++) && t%2==1, s+=p; k++; if(s%k==0, listput(v, k)); if(k>=lim, return(Vec(v)))))

Extensions

a(17) from Amiram Eldar, Jun 03 2024