A034956 Divide natural numbers in groups with prime(n) elements and add together.

3, 12, 40, 98, 253, 455, 850, 1292, 2047, 3335, 4495, 6623, 8938, 11180, 14335, 18815, 24249, 28731, 35845, 42884, 49348, 59408, 69139, 81791, 98164, 112211, 124939, 141026, 155434, 173681, 210439, 233966, 263040, 286062, 328098, 355152, 393442, 434558, 472777

Offset

1,1

Comments

Natural numbers starting from 1,2,3,4,...

Links

Hieronymus Fischer, Table of n, a(n) for n = 1..1000

Formula

From Hieronymus Fischer, Sep 27 2012: (Start)

a(n) = Sum_{k=A007504(n-1)+1..A007504(n)} k, n > 1.

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

a(n) = (A000217(A007504(n)) - A000217(A007504(n-1))), n > 0.

If we define A007504(0) := 0, then the formulas above are also true for n=1.

a(n) = (A034960(n) + A000040(n))/2.

a(n) = A034957(n) + A000040(n). (End)

Example

{1,2} #2 S=3;
{3,4,5} #3 S=12;
{6,7,8,9,10} #5 S=40;
{11,12,13,14,15,16,17} #7 S=98.

Maple

s:= proc(n) s(n):= `if`(n<1, 0, s(n-1)+ithprime(n)) end:
a:= n-> (t-> t(s(n))-t(s(n-1)))(i-> i*(i+1)/2):
seq(a(n), n=1..40);  # Alois P. Heinz, Mar 22 2023

Mathematica

Module[{nn=50, pr}, pr=Prime[Range[nn]]; Total/@TakeList[Range[ Total[ pr]], pr]](* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Oct 01 2017 *)

Prog

(Python)
from itertools import islice
from sympy import nextprime
def A034956_gen(): # generator of terms
    a, p = 0, 2
    while True:
        yield p*((a<<1)+p+1)>>1
        a, p = a+p, nextprime(p)
A034956_list = list(islice(A034956_gen(), 20)) # Chai Wah Wu, Mar 22 2023

Crossrefs

Cf. A006003, A027441, A034957.

Cf. A046992, A034958, A034959, A034960.

Cf. A000040, A000217, A007504.

Sequence in context: A062311 A303348 A237036 * A032093 A007993 A293366

Adjacent sequences: A034953 A034954 A034955 * A034957 A034958 A034959

Keyword

nonn,changed

Author

Patrick De Geest, Oct 15 1998

Status

approved