A034959 Divide even numbers into groups with prime(n) elements and add together.

2, 18, 70, 182, 484, 884, 1666, 2546, 4048, 6612, 8928, 13172, 17794, 22274, 28576, 37524, 48380, 57340, 71556, 85626, 98550, 118658, 138112, 163404, 196134, 224220, 249672, 281838, 310650, 347136, 420624, 467670, 525806, 571846, 655898

Offset: 1

Author

Patrick De Geest, Oct 15 1998

Keywords

• nonn

Examples

			{0,2} #2 S=2;
{4,6,8} #3 S=18;
{10,12,14,16,18} #5 S=70;
{20,22,24,26,28,30,32} #7 S=182.
		

Links

• Hieronymus Fischer, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006003, A027441, A034960.

Cf. A046992, A034956-A034958.

Programs

Python

from itertools import islice
from sympy import nextprime
def A034959_gen(): # generator of terms
    a, p = 0, 2
    while True:
        yield p*((a<<1)+p-1)
        a, p = a+p, nextprime(p)
A034959_list = list(islice(A034959_gen(),20)) # Chai Wah Wu, Mar 22 2023

Formula

From Hieronymus Fischer, Sep 27 2012: (Start)

a(n) = 2*Sum_{k=(A007504(n-1)+1)..A007504(n)} (k-1), n > 1.

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

a(n) = 2*(A000217(A007504(n) - 1) - A000217(A007504(n-1) - 1)), n > 1.

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

a(n) = 2*A034957(n).

a(n) = A034960(n) - A000040(n).

(End)