A151799 Version 2 of the "previous prime" function: largest prime < n.

2, 3, 3, 5, 5, 7, 7, 7, 7, 11, 11, 13, 13, 13, 13, 17, 17, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 29, 29, 31, 31, 31, 31, 31, 31, 37, 37, 37, 37, 41, 41, 43, 43, 43, 43, 47, 47, 47, 47, 47, 47, 53, 53, 53, 53, 53, 53, 59, 59, 61, 61, 61, 61, 61, 61, 67, 67, 67, 67, 71, 71, 73, 73, 73, 73

Offset: 3

Author

N. J. A. Sloane, Jun 29 2009

Keywords

• nonn
• easy
• nice

Comments

Version 1 of the "previous prime" function is "largest prime <= n". This produces A007917, the same sequence of numerical values, except the offset (or indexing) starts at 2 instead of 3.

Maple's "prevprime" function uses version 2.

See A007917 for references and further information.

Links

• Daniel Forgues, Table of n, a(n) for n = 3..100000

Crossrefs

Cf. A000040, A007917, A007918, A060265, A151800.

Programs

Haskell

a151799 = a007917 . (subtract 1)  -- Reinhard Zumkeller, Jul 26 2012

Maple

A151799:=n->prevprime(n): seq(A151799(n), n=3..100);

Mathematica

Table[NextPrime[n, -1], {n, 3, 77}] (* Jean-François Alcover, May 27 2011 *)

Maxima

makelist(prev_prime(n), n, 3, 79); /* Bruno Berselli, May 20 2011 */

PARI

a(n)=precprime(n-1) \\ Charles R Greathouse IV, Jul 12 2016

Python

from sympy import prevprime
def A151799(n):
    return prevprime(n) # Chai Wah Wu, Feb 28 2018

Formula

a(n) = A000040(A000720(n-1)). - Enrique Pérez Herrero, Jul 23 2011

a(n) = n + 1 - Sum_{k=1..n}( floor(k!^(n-1)/(n-1)!)-floor((k!^(n-1)-1)/(n-1)!) ). - Anthony Browne, May 17 2016

a(n) = A060265(floor(n/2)) for n >= 4. - Georg Fischer, Nov 29 2022