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%I #30 Jan 07 2017 02:49:28
%S 3,11,31,59,83,211,331,773,1297,1433,1471,1621,2027,2477,3637,4153,
%T 4787,4877,5623,7699,9103,9619,11743,12097,12959,13037,13591,13709,
%U 14177,14969,15299,16411,16703,16921,19463,19577,21379,22093,22721,24107,24151,24419,24509,24671,28657
%N Prime-Indexed Primes (PIPs) k such that the sum of all PIPs <= k is a prime.
%C This is a strict subset of A006450: {k from A006450 | Sum_{j=1..k} A006450(j) is prime}.
%C 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
%H Michael Turniansky, <a href="/A261148/b261148.txt">Table of n, a(n) for n = 1..508</a>
%e 11 is in the sequence because A006450(1) + A006450(2) + A006450(3) = 3 + 5 + 11 = 19, a prime number.
%t 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 *)
%o (APL (NARS200 dialect)) (0π+\A←¯2π¯2π⍳1000)/A
%o (PARI) lista(nn) = {s = 0; forprime(p=2, nn, q = prime(p); s += q; if (isprime(s), print1(q, ", ")););} \\ _Michel Marcus_, Aug 20 2015
%Y Cf. A006450.
%K nonn,easy
%O 1,1
%A _Michael Turniansky_, Aug 10 2015
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