A259408 a(1) = 1 thereafter a(n) = Sum_{m=1..n-1} prime(a(m)).

1, 2, 5, 16, 69, 416, 3277, 33590, 430131, 6700328, 124069971, 2680915918, 66579269891, 1876496610172, 59387269231505, 2091422223924852, 81321166136299741, 3467614972592015460

Offset: 1

Author

Anders Hellström, Jun 26 2015

Keywords

• nonn
• more

Crossrefs

Cf. A074271.

Programs

Mathematica

a = {1}; Do[AppendTo[a, Sum[Prime[a[[m]]], {m, n - 1}]], {n, 2, 15}];
a (* Michael De Vlieger, Aug 06 2015 *)

PARI

a(n) = if (n==1, 1, sum(k=1, n-1, prime(a(k)))); \\ Michel Marcus, Jun 26 2015

PARI

first(m)=my(v=vector(m)); v[1]=1; print1(1); for(i=2, m, v[i]=sum(k=1, i-1, prime(v[k])); print1(", ", v[i])); v; \\ Anders Hellström, Aug 01 2015

PARI

first(n)=my(v=vector(n,i,i)); for(i=3,n,v[i]=v[i-1]+prime(v[i-1])); v \\ Charles R Greathouse IV, Aug 06 2015

Perl

use bignum;
use Math::Prime::Util ':all';
print "1\n2\n";
my $a = 2;
while(1){
  $a += nth_prime($a);
  print "$a\n";
} # Charles R Greathouse IV, Aug 06 2015

Python

from sympy import prime
from functools import lru_cache
@lru_cache()
def a(n): return n if n < 3 else a(n-1) + prime(a(n-1))
print([a(n) for n in range(1, 14)]) # Michael S. Branicky, Oct 07 2022

Formula

a(n) = A014688(a(n-1)) for n>2, a(1)=1, a(2)=2.

Extensions

a(15) from Michael De Vlieger, Jul 01 2015

a(16)-a(18) from Charles R Greathouse IV, Aug 06 2015