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A108754
Difference between partial sum of the first n primes and n^2.
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
1,5
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
LINKS
FORMULA
a(n) = A007504(n) - A000290(n).
EXAMPLE
a(5) = A007504(5) - A000290(5) = 28 - (5^2) = 3.
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 *)
PROG
(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
CROSSREFS
Partial sums of A131733.
Sequence in context: A102378 A118026 A248956 * A033499 A267262 A106607
KEYWORD
easy,nonn
AUTHOR
Alexandre Wajnberg, Jun 23 2005
EXTENSIONS
Edited and extended by Robert G. Wilson v, Jun 25 2005
STATUS
approved