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A034957
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Divide natural numbers in groups with prime(n) elements and add together.
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4
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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
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OFFSET
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1,2
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COMMENTS
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Natural numbers starting from 0,1,2,3,...
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LINKS
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FORMULA
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From _Hieronymus Fischer_, Sep 27 2012: (Start)
If we define A007504(0):=0, then the formulas above are also true for n=1.
(End)
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EXAMPLE
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{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.
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MATHEMATICA
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{1}~Join~Map[Abs@ Apply[Subtract, Map[PolygonalNumber, #]] &, Partition[Accumulate@ Prime@ Range@ 37 - 1, 2, 1]] (* _Michael De Vlieger_, Oct 06 2019 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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_Patrick De Geest_, Oct 15 1998
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STATUS
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approved
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