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a(1) = 1 thereafter a(n) = Sum_{m=1..n-1} prime(a(m)).
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%I #57 Oct 07 2022 20:03:46

%S 1,2,5,16,69,416,3277,33590,430131,6700328,124069971,2680915918,

%T 66579269891,1876496610172,59387269231505,2091422223924852,

%U 81321166136299741,3467614972592015460

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

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

%t a = {1}; Do[AppendTo[a, Sum[Prime[a[[m]]], {m, n - 1}]], {n, 2, 15}];

%t a (* _Michael De Vlieger_, Aug 06 2015 *)

%o (PARI) a(n) = if (n==1, 1, sum(k=1, n-1, prime(a(k)))); \\ _Michel Marcus_, Jun 26 2015

%o (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

%o (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

%o (Perl) use bignum;

%o use Math::Prime::Util ':all';

%o print "1\n2\n";

%o my $a = 2;

%o while(1){

%o $a += nth_prime($a);

%o print "$a\n";

%o } # _Charles R Greathouse IV_, Aug 06 2015

%o (Python)

%o from sympy import prime

%o from functools import lru_cache

%o @lru_cache()

%o def a(n): return n if n < 3 else a(n-1) + prime(a(n-1))

%o print([a(n) for n in range(1, 14)]) # _Michael S. Branicky_, Oct 07 2022

%Y Cf. A074271.

%K nonn,more

%O 1,2

%A _Anders Hellström_, Jun 26 2015

%E a(15) from _Michael De Vlieger_, Jul 01 2015

%E a(16)-a(18) from _Charles R Greathouse IV_, Aug 06 2015