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A273932
Integers m such that ceiling(sqrt(m!)) is prime.
0
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).
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
KEYWORD
nonn,more
AUTHOR
Salvador Cerdá, Jun 04 2016
EXTENSIONS
a(9) from Giovanni Resta, Jun 20 2016
STATUS
approved