A096071 Primes arising as a partial sum of A096070.

3, 11, 23, 41, 67, 83, 109, 137, 173, 223, 269, 311, 359, 409, 467, 541, 607, 677, 751, 829, 907, 991, 1087, 1181, 1277, 1381, 1487, 1601, 1721, 1847, 1973, 2099, 2237, 2371, 2521, 2659, 2801, 2953, 3109, 3257, 3433, 3593, 3767, 3947, 4111, 4297, 4481

Offset

1,1

Comments

The n-th partial sum of A096070 is prime iff n is even.

Links

Table of n, a(n) for n=1..47.

Example

The sixth partial sum of A096070 is 1+2+3+5+4+8 = 23.

Mathematica

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 *)

Prog

(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)))}

Crossrefs

Cf. A096070.

Sequence in context: A289575 A086497 A121509 * A230117 A342174 A159791

Adjacent sequences: A096068 A096069 A096070 * A096072 A096073 A096074

Keyword

nonn

Author

Amarnath Murthy, Jun 20 2004

Extensions

Edited, corrected and extended by Klaus Brockhaus, Jun 21 2004

Status

approved