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

3,1

Comments

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

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.

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A055211.

Sequence in context: A145987 A088083 A116457 * A282632 A212912 A356751

Adjacent sequences: A037152 A037153 A037154 * A037156 A037157 A037158

Keyword

nonn

Author

Jud McCranie

Extensions

More terms from James A. Sellers, Jul 06 2000

Status

approved