A263541 Numbers k such that k divides the sum of the first k primes with prime indices.

1, 2, 4, 6, 40, 43, 705, 789, 1148, 2140, 4276, 5512, 6672, 8754, 38434, 174501, 493578, 598249, 628064, 702774, 1368196, 4584004, 13813057, 36425906, 87964443, 447997476, 1964288296

Offset: 1

Author

Altug Alkan, Oct 20 2015

Keywords

• nonn

Comments

There are 8 values of a(n) < 1000 although A045345 has 4 values A045345(n) < 1000. How do these sequences compare asymptotically?

Heuristics suggest that the ratio of the number of terms in each sequence up to x should approach 1 as x increases without bound. In the Cramér model, log a(n) and log A045345(n) are Erlang-distributed with shape n and rate 1. - Charles R Greathouse IV, Oct 20 2015

Examples

			1 is in the sequence because prime(prime(1)) = 3 is divisible by 1.
2 is in the sequence because prime(prime(1)) + prime(prime(2)) = 3 + 5 = 8 is divisible by 2.
		

Crossrefs

Cf. A006450, A045345, A083186.

Programs

PARI

list(lim)=my(v=List(),k,s,t); forprime(p=2,, if(isprime(t++), s+=p; k++; if(s%k==0, listput(v, k)); if(k>=lim, return(Vec(v))))) \\ Charles R Greathouse IV, Oct 20 2015

Extensions

a(12)-a(26) from Charles R Greathouse IV, Oct 20 2015

a(27) from Charles R Greathouse IV, Oct 21 2015