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

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..9.

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A281233 A048459 A203615 * A270831 A063738 A063737

Adjacent sequences: A273929 A273930 A273931 * A273933 A273934 A273935

Keyword

nonn,more

Author

Salvador Cerdá, Jun 04 2016

Extensions

a(9) from Giovanni Resta, Jun 20 2016

Status

approved