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A034957 Divide natural numbers in groups with prime(n) elements and add together. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Natural numbers starting from 0,1,2,3,...
LINKS
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
Sequence in context: A212099 A212100 A005898 * A180082 A002418 A118414
KEYWORD
nonn
AUTHOR
Patrick De Geest, Oct 15 1998
STATUS
approved

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Last modified July 19 22:34 EDT 2024. Contains 374441 sequences. (Running on oeis4.)