A263546 Numbers k such that k divides the sum of the first k primes with even indices.

1, 2, 6, 12, 15, 28, 40, 92, 111, 113, 145, 223, 268, 420, 625, 2080, 2282, 2996, 3371, 19560, 38032, 54426, 1474778, 3763906, 5196340, 6435993, 7808592, 11487666, 16738298, 28145334, 53830258, 57281504, 77275294, 135770496, 164914949

Offset

1,2

Comments

There are 15 values of a(n) < 1000 although A045345 has 4 values A045345(n) < 1000. How do these sequences compare asymptotically?

Links

Table of n, a(n) for n=1..35.

Example

1 is in the sequence because prime(2) = 3 is divisible by 1.
2 is in the sequence because prime(2) + prime(4) = 3 + 7 = 10 is divisible by 2.

Mathematica

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

Prog

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

Crossrefs

Cf. A031215, A045345, A077126, A263541.

Sequence in context: A065154 A354757 A230482 * A143408 A191331 A367465

Adjacent sequences: A263543 A263544 A263545 * A263547 A263548 A263549

Keyword

nonn

Author

Altug Alkan, Oct 20 2015

Status

approved