A273932 Integers m such that ceiling(sqrt(m!)) is prime.

2, 3, 4, 5, 7, 21, 2132, 3084, 9301

Offset: 1

Author

Salvador Cerdá, Jun 04 2016

Keywords

• nonn
• more
• hard

Comments

This sequence includes the known solutions of Brocard's problem as of 2016 (see A146968).

Examples

			3 is a term because 3! = 6, sqrt(6) = 2.449489742783178..., the ceiling of which is 3, which is prime.
4 is a term because 4! = 24, sqrt(24) = 4.898979485566356..., the ceiling of which is 5, which is prime.
		

Crossrefs

Cf. A055228 (ceiling(sqrt(n!))), A146968.

Programs

Mathematica

Select[Range[3200], PrimeQ[Ceiling[Sqrt[#!]]] &]

Python

from math import isqrt, factorial
from itertools import count, islice
from sympy import isprime
def A273932_gen(): # generator of terms
    return filter(lambda n:isprime(1+isqrt(factorial(n)-1)),count(1))
A273932_list = list(islice(A273932_gen(),7)) # Chai Wah Wu, Jul 29 2022

Extensions

a(9) from Giovanni Resta, Jun 20 2016