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%I #15 Mar 28 2021 07:03:36
%S 3,5,11,13,17,37,41,61,83,97,101,127,131,139,167,181,233,241,251,307,
%T 311,331,353,421,431,433,443,457,461,487,509,523,557,601,617,727,743,
%U 751,761,823,881,919,941,1021,1031,1033,1049,1051,1061,1093,1103,1117
%N 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.
%C Initial prime p=3.
%H Amiram Eldar, <a href="/A178604/b178604.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%p 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
%t 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 *)
%K nonn
%O 1,1
%A Ryan Stratford (rstratfo(AT)gmail.com), May 30 2010, May 31 2010
%E Corrected by Ryan Stratford (rstratfo(AT)gmail.com), May 31 2010
%E a(36) onwards from _Robert G. Wilson v_, Jun 08 2010
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