A034957 Divide natural numbers in groups with prime(n) elements and add together.

1, 9, 35, 91, 242, 442, 833, 1273, 2024, 3306, 4464, 6586, 8897, 11137, 14288, 18762, 24190, 28670, 35778, 42813, 49275, 59329, 69056, 81702, 98067, 112110, 124836, 140919, 155325, 173568, 210312, 233835, 262903, 285923, 327949, 355001, 393285

Offset

1,2

Comments

Natural numbers starting from 0,1,2,3,...

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-1), n > 1.

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

a(n) = (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) = A034959(n)/2.

a(n) = A034956(n) - A000040(n).

(End)

Example

{0,1} #2 S=1;
{2,3,4} #3 S=9;
{5,6,7,8,9} #5 S=35;
{10,11,12,13,14,15,16} #7 S=91.

Mathematica

{1}~Join~Map[Abs@ Apply[Subtract, Map[PolygonalNumber, #]] &, Partition[Accumulate@ Prime@ Range@ 37 - 1, 2, 1]] (* Michael De Vlieger, Oct 06 2019 *)

Prog

(Python)
from itertools import islice
from sympy import nextprime
def A034957_gen(): # generator of terms
    a, p = 0, 2
    while True:
        yield p*((a<<1)+p-1)>>1
        a, p = a+p, nextprime(p)
A034957_list = list(islice(A034957_gen(), 20)) # Chai Wah Wu, Mar 22 2023

Crossrefs

Cf. A006003, A027441, A034956.

Cf. A046992, A034958, A034959, A034960.

Sequence in context: A212099 A212100 A005898 * A180082 A002418 A118414

Adjacent sequences: A034954 A034955 A034956 * A034958 A034959 A034960

Keyword

nonn

Author

Patrick De Geest, Oct 15 1998

Status

approved