A083186 Sum of the first n primes whose indices are primes.

3, 8, 19, 36, 67, 108, 167, 234, 317, 426, 553, 710, 889, 1080, 1291, 1532, 1809, 2092, 2423, 2776, 3143, 3544, 3975, 4436, 4945, 5492, 6055, 6642, 7241, 7858, 8567, 9306, 10079, 10876, 11735, 12612, 13531, 14498, 15489, 16520, 17583, 18670, 19823

Offset

1,1

Comments

Partial sums of A006450.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Formula

a(n) = Sum_{k=1..n} prime(prime(k)).

a(n) ~ (n log n)^2 / 2. - Charles R Greathouse IV, Oct 20 2015

Mathematica

Accumulate[Prime[Prime[Range[50]]]] (* Harvey P. Dale, Jun 24 2012 *)

Prog

(PARI) pipsum(n)=s=0; sr=0; for(x=1, n, y=prime(prime(x)); s+=y; print1(s" "); sr+=1.0/y; ); print(); print(sr)
(PARI) a(n)=my(i, j, s); forprime(p=2, , if(isprime(i++), s+=p; if(j++==n, return(s)))) \\ Charles R Greathouse IV, Oct 20 2015
(PARI) first(n)=my(v=vector(n), i, j, s); forprime(p=2, , if(isprime(i++), s+=p; v[j++]=s; if(j==n, return(v)))) \\ Charles R Greathouse IV, Oct 20 2015

Crossrefs

Cf. A006450, A109790.

Sequence in context: A147358 A209367 A086167 * A055341 A067332 A082535

Adjacent sequences: A083183 A083184 A083185 * A083187 A083188 A083189

Keyword

nonn

Author

Cino Hilliard, Jun 01 2003

Status

approved