A111267 Let q(n) = prime(1) + ... + prime(n); a(n) = smallest divisor of q(n) not already in sequence.

1, 5, 2, 17, 4, 41, 29, 7, 10, 3, 8, 197, 14, 281, 82, 127, 11, 167, 71, 9, 89, 113, 19, 107, 20, 27, 16, 457, 37, 59, 40, 617, 28, 709, 569, 809, 34, 67, 31, 21, 23, 383, 214, 1277, 38, 1409, 317, 79, 13, 43, 25, 69, 22, 2027, 3169, 161, 6, 193, 3709, 7699, 26, 331, 613, 8893

Offset: 1

Author

N. J. A. Sloane, Nov 03 2005

Keywords

• nonn

Comments

Does every number appear?

A basic sequence related to additive structure of primes.

Links

• Donovan Johnson, Table of n, a(n) for n = 1..10000

Crossrefs

For records see A111268, A111084. For inverse see A111229.

Programs

Maple

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)];

Mathematica

Fold[Function[{l, d}, Append[l, SelectFirst[d, FreeQ[l, #] &]]], {}, Divisors@Accumulate@Prime@Range[100]] (* Virgile Andreani, Jul 11 2016 *)