A060698 The sum of the first n composite numbers minus 1 is a prime.

1, 3, 11, 15, 22, 39, 51, 57, 66, 67, 71, 79, 98, 105, 108, 109, 115, 118, 119, 125, 135, 150, 151, 152, 156, 160, 169, 200, 201, 205, 211, 223, 228, 241, 271, 281, 282, 291, 312, 315, 322, 331, 341, 350, 372, 382, 385, 395, 401, 420, 433, 461, 482, 498, 544

Offset: 1

Author

Robert G. Wilson v, Apr 20 2001

Keywords

• nonn

Programs

Mathematica

Composite[ n_Integer ] := (k = n + PrimePi[ n ] + 1; While[ k - PrimePi[ k ] - 1 != n, k++ ]; k); Select[ Range[ 1000 ], PrimeQ[ Sum[ Composite[ k ], {k, 1, #} ] - 1 ] & ]
Position[Accumulate[Select[Range[700],CompositeQ]]-1,?PrimeQ]//Flatten (* _Harvey P. Dale, Jul 20 2016 *)