A346425 a(n) is the greatest number k such that k! <= prime(n).

2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 1

Author

Bernard Schott, Jul 16 2021

Keywords

• nonn

Comments

Terms 2, 3, 4, 5, ... appear respectively 3, 6, 21, 98, ... times consecutively; indeed, 2 appears A061232(1) + A061232(2) times, then every m >= 3 appears A061232(m) times.

Examples

			prime(1) = 2 and the greatest k with k! <= 2 is 2, so a(1) = 2.
prime(4) = 7 and the greatest k with k! <= 7 is 3, so a(4) = 3.
prime(10) = 29 and the greatest k with k! <= 29 is 4 so a(10) = 4.
Rows with n, prime(n), greatest k! <=n, a(n) for n = 1..14
      n        1    2    3    4    5    6    7    8    9   10   11   12   13   14
   prime(n)    2    3    5    7   11   13   17   19   23   29   31   37   41   43
  greatest k!  2    2    2    6    6    6    6    6    6   24   24   24   24   24
    a(n)       2    2    2    3    3    3    3    3    3    4    4    4    4    4
		

Crossrefs

Cf. A000040, A061232, A136437.

Programs

PARI

a(n) = my(k=1); until (k! > prime(n), k++); k-1; \\ Michel Marcus, Jul 19 2021

Formula

a(n)! = A000040(n) - A136437(n).