A037155 a(n) = n!-p, where p is the largest prime < (n!-1).

3, 5, 7, 11, 17, 31, 13, 11, 13, 13, 23, 17, 47, 53, 59, 41, 101, 31, 31, 73, 89, 73, 149, 37, 43, 101, 31, 79, 61, 163, 47, 193, 113, 127, 97, 79, 73, 83, 131, 79, 109, 109, 53, 89, 79, 103, 59, 97, 179, 67, 59, 127, 61, 461, 277, 109, 137, 139, 71, 71, 101, 359

Offset: 3

Author

Jud McCranie

Keywords

• nonn

Comments

Analogous to the lesser Fortunate numbers and like them, all entries so far are primes.

Examples

			a(4) = 4!-19 = 24-19 = 5.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 3..1000
• Antonín Čejchan, Michal Křížek, and Lawrence Somer, On Remarkable Properties of Primes Near Factorials and Primorials, Journal of Integer Sequences, Vol. 25 (2022), Article 22.1.4.

Crossrefs

Cf. A055211.

Programs

Mathematica

PrevPrime[ n_Integer ] := (k=n-1; While[ !PrimeQ[ k ], k-- ]; Return[ k ]); f[ n_Integer ] := (p = n! - 1; q = NextPrime[ p ]; Return[ p - q + 1 ]); Table[ f[ n ], {n, 3, 75} ]
f[n_]:=Module[{nf=n!},nf-NextPrime[nf-1,-1]];f/@Range[3,90]  (* Harvey P. Dale, Mar 20 2011 *)

PARI

a(n)=my(N=n!); N-precprime(N-3) \\ Charles R Greathouse IV, Jan 28 2018

Python

from sympy import factorial, prevprime
def a(n): fn = factorial(n); return fn - prevprime(fn-1)
print([a(n) for n in range(3, 65)]) # Michael S. Branicky, May 22 2022

Formula

a(n) >= n. - Seiichi Manyama, Mar 21 2018

Extensions

More terms from James Sellers, Jul 06 2000