A178604 Increasing prime numbers p such that p does not divide the sum of the previous primes (p included) with the same property. We include the initial exception when p=3.

3, 5, 11, 13, 17, 37, 41, 61, 83, 97, 101, 127, 131, 139, 167, 181, 233, 241, 251, 307, 311, 331, 353, 421, 431, 433, 443, 457, 461, 487, 509, 523, 557, 601, 617, 727, 743, 751, 761, 823, 881, 919, 941, 1021, 1031, 1033, 1049, 1051, 1061, 1093, 1103, 1117

Offset

1,1

Comments

Initial prime p=3.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

3+5 = 8 is not divisible by 3 or 5. However, 3+5+7 = 15 is divisible by 3 and 5, so we omit 7. Similarly, 3+5+11+13+17+19 = 68 is divisible by 17, so we omit 19.

Maple

count := 1; t := nextprime(2); sum1 := t; prod1 := t; while count < 100 do t := nextprime(t); while gcd(prod1*t, sum1+t) > 1 do t := nextprime(t) end do; prod1 := prod1*t; sum1 := sum1+t; count := count+1 print(t); end do

Mathematica

p = 3; lst = {3}; fQ[n_] := Block[{k = 1, ln = 2 + Length@lst, s = n + Plus @@ lst}, AppendTo[lst, n]; While[Mod[s, lst[[k]]] != 0, k++ ]; If[k != ln, lst = Most@lst]]; While[p = NextPrime@p; p < 1150, fQ@p]; lst (* Robert G. Wilson v, Jun 08 2010 *)

Crossrefs

Sequence in context: A250481 A227011 A243627 * A153443 A211876 A066587

Adjacent sequences: A178601 A178602 A178603 * A178605 A178606 A178607

Keyword

nonn

Author

Ryan Stratford (rstratfo(AT)gmail.com), May 30 2010, May 31 2010

Extensions

Corrected by Ryan Stratford (rstratfo(AT)gmail.com), May 31 2010

a(36) onwards from Robert G. Wilson v, Jun 08 2010

Status

approved