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

1,2

Links

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

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

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 *)

Prog

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

Crossrefs

Cf. A007504 (Sum of first n primes).

Sequence in context: A262744 A359516 A347703 * A037032 A165753 A347779

Adjacent sequences: A112994 A112995 A112996 * A112998 A112999 A113000

Keyword

nonn

Author

Zak Seidov, Jan 03 2006

Extensions

More terms from Michel Marcus, Oct 09 2013

Status

approved