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 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. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Initial prime p=3. LINKS EXAMPLE 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

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Last modified May 23 10:51 EDT 2019. Contains 323513 sequences. (Running on oeis4.)