A112997 Sum of first n primes minus sum of their indices.

1, 2, 4, 7, 13, 20, 30, 41, 55, 74, 94, 119, 147, 176, 208, 245, 287, 330, 378, 429, 481, 538, 598, 663, 735, 810, 886, 965, 1045, 1128, 1224, 1323, 1427, 1532, 1646, 1761, 1881, 2006, 2134, 2267, 2405, 2544, 2692, 2841, 2993, 3146, 3310, 3485, 3663, 3842

Offset: 1

Author

Zak Seidov, Jan 03 2006

Keywords

• nonn

Links

• Michel Marcus, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007504 (Sum of first n primes).

Programs

Mathematica

Table[Total[Take[Table[Prime[n]-n, {n, 1, 20}], i]], {i, 20}]
With[{nn=50},Accumulate[Prime[Range[nn]]]-Accumulate[Range[nn]]] (* Harvey P. Dale, Aug 31 2023 *)

PARI

a(n) = sum(i=1, n, prime(i)-i); \\ Michel Marcus, Oct 09 2013

Formula

a(n) = A007504(n) - n(n+1)/2.

a(n) = Sum_{k=1..n} A014689(n) = partial sums of A014689. - Philippe Lallouet (philip.lallouet(AT)orange.fr), Aug 27 2008

Extensions

More terms from Michel Marcus, Oct 09 2013