A261148 Prime-Indexed Primes (PIPs) k such that the sum of all PIPs <= k is a prime.

3, 11, 31, 59, 83, 211, 331, 773, 1297, 1433, 1471, 1621, 2027, 2477, 3637, 4153, 4787, 4877, 5623, 7699, 9103, 9619, 11743, 12097, 12959, 13037, 13591, 13709, 14177, 14969, 15299, 16411, 16703, 16921, 19463, 19577, 21379, 22093, 22721, 24107, 24151, 24419, 24509, 24671, 28657

Offset: 1

Author

Michael Turniansky, Aug 10 2015

Keywords

• nonn
• easy

Comments

This is a strict subset of A006450: {k from A006450 | Sum_{j=1..k} A006450(j) is prime}.

It seems from observation that asymptotically a(n)/A006450(n) ~ 7.5*log(n) - e. But might this just be coincidence? I certainly have no proof. - Michael Turniansky, Aug 21 2015

Examples

			11 is in the sequence because A006450(1) + A006450(2) + A006450(3) = 3 + 5 + 11 = 19, a prime number.
		

Links

• Michael Turniansky, Table of n, a(n) for n = 1..508

Crossrefs

Cf. A006450.

Programs

Mathematica

L={}; s=0; p=2; While[Length@L < 100, If[PrimeQ[s+=(q = Prime@p)], AppendTo[L, q]]; p = NextPrime@ p]; L (* Giovanni Resta, Aug 21 2015 *)

PARI

lista(nn) = {s = 0; forprime(p=2, nn, q = prime(p); s += q; if (isprime(s), print1(q, ", ")););} \\ Michel Marcus, Aug 20 2015