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

1,1

Links

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

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)

Example

{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.

Prog

(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

Crossrefs

Cf. A006003, A027441, A034960.

Cf. A046992, A034956-A034958.

Sequence in context: A112365 A242200 A258929 * A316902 A316904 A196812

Adjacent sequences: A034956 A034957 A034958 * A034960 A034961 A034962

Keyword

nonn

Author

Patrick De Geest, Oct 15 1998

Status

approved