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A178604
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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.
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1
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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
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OFFSET
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1,1
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COMMENTS
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Initial prime p=3.
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LINKS
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EXAMPLE
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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.
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Ryan Stratford (rstratfo(AT)gmail.com), May 30 2010, May 31 2010
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EXTENSIONS
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Corrected by Ryan Stratford (rstratfo(AT)gmail.com), May 31 2010
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STATUS
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approved
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