%I #12 Jul 12 2016 05:31:44
%S 1,5,2,17,4,41,29,7,10,3,8,197,14,281,82,127,11,167,71,9,89,113,19,
%T 107,20,27,16,457,37,59,40,617,28,709,569,809,34,67,31,21,23,383,214,
%U 1277,38,1409,317,79,13,43,25,69,22,2027,3169,161,6,193,3709,7699,26,331,613,8893
%N Let q(n) = prime(1) + ... + prime(n); a(n) = smallest divisor of q(n) not already in sequence.
%C Does every number appear?
%C A basic sequence related to additive structure of primes.
%H Donovan Johnson, <a href="/A111267/b111267.txt">Table of n, a(n) for n = 1..10000</a>
%p with(numtheory); M:=500; p0:=2; a[1]:=1; for n from 2 to M do p0:=p0+ithprime(n); t1:=divisors(p0); t2:=nops(t1); for i from 1 to t2 do d:=t1[i]; hit:=0; for j from 1 to n-1 do if a[j]=d then hit:=1; break; fi; od: if hit = 0 then a[n]:=d; break; fi; od: od: s1:=[seq(a[n],n=1..M)];
%t Fold[Function[{l, d}, Append[l, SelectFirst[d, FreeQ[l, #] &]]], {}, Divisors@Accumulate@Prime@Range[100]] (* _Virgile Andreani_, Jul 11 2016 *)
%Y For records see A111268, A111084. For inverse see A111229.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Nov 03 2005