A350174 For k = 0, 1, 2, 3, ... write k prime(k+1) times.

0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset: 0

Author

Michel Marcus, Dec 18 2021

Keywords

• nonn
• easy

Comments

a(n) = k is the largest k with sum of primes A007504(k) <= n. - Kevin Ryde, Apr 19 2022

References

• J.-P. Delahaye, Des suites fractales d’entiers, Pour la Science, No. 531 January 2022. Sequence g) p. 82.

Crossrefs

Cf. A000040, A007504.

Essentially the same as A083375.

Programs

Maple

a:=[];
for n from 0 to 10 do a:=[op(a), seq(n,i=1..ithprime(n+1))]; od:
a; # N. J. A. Sloane, Dec 18 2021

Python

from itertools import count, islice, chain
from sympy import prime
def A350174gen(): return chain.from_iterable([k]*prime(k+1) for k in count(0))
A350174_list = list(islice(A350174gen(),50)) # Chai Wah Wu, Dec 19 2021

Formula

a(n) = A083375(n+1) - 1. - Peter Munn, May 26 2023