A108754 Difference between partial sum of the first n primes and n^2.

1, 1, 1, 1, 3, 5, 9, 13, 19, 29, 39, 53, 69, 85, 103, 125, 151, 177, 207, 239, 271, 307, 345, 387, 435, 485, 535, 587, 639, 693, 759, 827, 899, 971, 1051, 1131, 1215, 1303, 1393, 1487, 1585, 1683, 1789, 1895, 2003, 2111, 2229, 2357, 2487, 2617, 2749, 2885, 3021

Offset: 1

Author

Alexandre Wajnberg, Jun 23 2005

Keywords

• easy
• nonn

Comments

Also difference between partial sum of the first n primes and the sum of the first n odd numbers. - Cino Hilliard, Dec 02 2007

Examples

			a(5) = A007504(5) - A000290(5) = 28 - (5^2) = 3.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000290, A007504.

Partial sums of A131733.

Programs

Mathematica

Table[ Sum[ Prime[i], {i, n}] - n^2, {n, 53}] (* Robert G. Wilson v, Jun 25 2005 *)
Module[{nn=60,prs},prs=Accumulate[Prime[Range[nn]]];#[[1]]-#[[2]]&/@Thread[ {prs,Range[ nn]^2}]] (* Harvey P. Dale, Aug 14 2024 *)

PARI

g(n) = for(x=1,n,y=sum(j=1,x,2*j-1);z=sum(j=1,x,prime(j));print1(z-y",")) \\ Cino Hilliard, Dec 02 2007

Formula

a(n) = A007504(n) - A000290(n).

Extensions

Edited and extended by Robert G. Wilson v, Jun 25 2005