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

1,2

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

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 *)

Crossrefs

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

Sequence in context: A213582 A364108 A367290 * A282067 A281842 A282224

Adjacent sequences: A111264 A111265 A111266 * A111268 A111269 A111270

Keyword

nonn

Author

N. J. A. Sloane, Nov 03 2005

Status

approved