%I #6 Nov 03 2020 17:59:40
%S 3,11,23,41,67,83,109,137,173,223,269,311,359,409,467,541,607,677,751,
%T 829,907,991,1087,1181,1277,1381,1487,1601,1721,1847,1973,2099,2237,
%U 2371,2521,2659,2801,2953,3109,3257,3433,3593,3767,3947,4111,4297,4481
%N Primes arising as a partial sum of A096070.
%C The n-th partial sum of A096070 is prime iff n is even.
%e The sixth partial sum of A096070 is 1+2+3+5+4+8 = 23.
%t Module[{n, m = 100, s = 0, v = {}}, Reap[For[n = 1, n <= m, n++, k = 1; While[MemberQ[v, k] || PrimeQ[s + k] != EvenQ[n], k++]; If[PrimeQ[s], Sow[s]]; s = s + k; v = Union[v, {k}]]][[2, 1]]] (* _Jean-François Alcover_, Nov 03 2020, after PARI *)
%o (PARI) {m=94;s=0;v=Set([]);for(n=1,m,k=1;while(setsearch(v,k)>0||isprime(s+k)!=(n%2==0),k++);s=s+k;if(n%2==0,print1(s,","));v=setunion(v,Set(k)))}
%Y Cf. A096070.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Jun 20 2004
%E Edited, corrected and extended by _Klaus Brockhaus_, Jun 21 2004
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