The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A034956 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A034956

Divide natural numbers in groups with prime(n) elements and add together.
(history; published version)

#35 by Andrey Zabolotskiy at Thu Apr 25 09:09:36 EDT 2024

STATUS

editing

approved

#34 by Andrey Zabolotskiy at Thu Apr 25 09:09:34 EDT 2024

FORMULA

a(n) = A034957(n) + A000040(n). (End)

STATUS

approved

editing

#33 by Alois P. Heinz at Wed Mar 22 13:21:10 EDT 2023

STATUS

editing

approved

#32 by Alois P. Heinz at Wed Mar 22 13:20:48 EDT 2023

CROSSREFS

Cf. A000040, A000217, A007504.

#31 by Alois P. Heinz at Wed Mar 22 13:19:17 EDT 2023

MAPLE

s:= proc(n) s(n):= `if`(n<1, 0, s(n-1)+ithprime(n)) end:

a:= n-> (t-> t(s(n))-t(s(n-1)))(i-> i*(i+1)/2):

seq(a(n), n=1..40); # Alois P. Heinz, Mar 22 2023

#30 by Alois P. Heinz at Wed Mar 22 13:18:52 EDT 2023

DATA

3, 12, 40, 98, 253, 455, 850, 1292, 2047, 3335, 4495, 6623, 8938, 11180, 14335, 18815, 24249, 28731, 35845, 42884, 49348, 59408, 69139, 81791, 98164, 112211, 124939, 141026, 155434, 173681, 210439, 233966, 263040, 286062, 328098, 355152, 393442, 434558, 472777

STATUS

proposed

editing

#29 by Michel Marcus at Wed Mar 22 13:05:27 EDT 2023

STATUS

editing

proposed

#28 by Michel Marcus at Wed Mar 22 13:05:24 EDT 2023

EXAMPLE

{1,2} #2 S=3;

{3,4,5} #3 S=12;

{6,7,8,9,10} #5 S=40;

{1,2} #2 S=3; {3,4,5} #3 S=12; {6,7,8,9,10} #5 S=40; {11,12,13,14,15,16,17} #7 S=98; etc.

STATUS

proposed

editing

#27 by Chai Wah Wu at Wed Mar 22 10:17:17 EDT 2023

STATUS

editing

proposed

#26 by Chai Wah Wu at Wed Mar 22 10:17:11 EDT 2023

PROG

(Python)

from itertools import islice

from sympy import nextprime

def A034956_gen(): # generator of terms

a, p = 0, 2

while True:

yield p*((a<<1)+p+1)>>1

a, p = a+p, nextprime(p)

A034956_list = list(islice(A034956_gen(), 20)) # Chai Wah Wu, Mar 22 2023

STATUS

approved

editing