A075557 a(n) is the smallest odd prime such that (1) a(n) doesn't already appear in the sequence; (2) the n-th partial sum is divisible by n; and (3) the n-th partial sum is relatively prime to n+1.

3, 5, 7, 13, 37, 31, 23, 17, 53, 11, 251, 29, 79, 43, 73, 61, 97, 67, 107, 173, 59, 103, 199, 163, 71, 149, 47, 101, 509, 89, 151, 283, 229, 271, 211, 109, 257, 113, 269, 157, 241, 331, 83, 389, 41, 313, 1543, 19, 307, 463, 373, 277, 811, 457, 137, 191, 419, 311, 197

Offset: 1

Author

Amarnath Murthy, Sep 24 2002

Keywords

• nonn
• easy
• look

Comments

Condition (3) is needed to ensure that a(n+1) exists.

Examples

			a(5)=37: The 4th partial sum is 28. 7 is the smallest odd prime that satisfies (2) (28+7=35), but 7 has already been used. 17 satisfies (1) and (2) (28+17=45), but 45+a(6) must be a multiple of 6 and the only odd prime satisfying that requirement is 3, which has already been used. 37 works (28+37=65).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A065091 (odd primes).

Programs

Maple

N:= 10000: # for terms until the first term > N.
Cands:= select(isprime, [seq(i,i=3..N,2)]):
nC:= nops(Cands):
R:= NULL: s:= 0:
for n from 1 do
  found:= false;
  for i from 1 to nC do
    if s + Cands[i] mod n = 0 and igcd(s + Cands[i],n+1) = 1 then
       R:= R, Cands[i];
       s:= s + Cands[i];
       Cands:= subsop(i=NULL,Cands);
       nC:= nC-1;
       found:= true;
       break
     fi
  od;
  if not found then break fi
od:
R; # Robert Israel, Dec 07 2024

Extensions

Edited by David Wasserman, Jun 27 2003

Corrected by Robert Israel, Dec 07 2024