A099850 Partial sums of A004648.

0, 1, 3, 6, 7, 8, 11, 14, 19, 28, 37, 38, 40, 41, 43, 48, 56, 63, 73, 84, 94, 107, 121, 138, 160, 183, 205, 228, 250, 273, 276, 279, 284, 287, 296, 303, 312, 323, 334, 347, 362, 375, 394, 411, 428, 443, 466, 497, 528, 557, 586, 617, 646, 681, 718, 757, 798, 837

Offset

1,3

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{k=1..n} A004648(k).

Example

A004648 begins: 0, 1, 2, 3, 1, 1, 3, 3, 5, 9, 9, ... so the partial sums are 0, 1, 3, 6, 7, 8, 11, 14, 19, 28, 37, ...

Mathematica

Table[Sum[Mod[Prime[j], j], {j, n}], {n, 100}] (* G. C. Greubel, Apr 20 2023 *)
Accumulate[Table[Mod[Prime[n], n], {n, 100}]] (* Harvey P. Dale, Jun 14 2023 *)

Prog

(PARI) s=vector(100):s[1]=prime(1)%1:for(n=2, 100, s[n]=s[n-1]+prime(n)%n)
(Magma) [(&+[(NthPrime(k) mod k): k in [1..n]]): n in [1..100]]; // G. C. Greubel, Apr 20 2023
(SageMath)
def A004648(n): return (nth_prime(n)%n)
def A099850(n): return sum(A004648(k) for k in range(1, n+1))
[A099850(n) for n in range(1, 101)] # G. C. Greubel, Apr 20 2023

Crossrefs

Cf. A004648.

Sequence in context: A047557 A342736 A284390 * A310132 A189659 A157041

Adjacent sequences: A099847 A099848 A099849 * A099851 A099852 A099853

Keyword

easy,nonn

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Oct 27 2004

Status

approved