A267016 Numbers that satisfy: (isqrt(n)-1)! = isqrt(n)-1 mod isqrt(n).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181

Offset

1,2

Comments

Numbers n such that A000196(n) is in A008578 (i.e. is either 1 or prime). - Robert Israel, Jan 09 2016

Links

Daniel Suteu, Table of n, a(n) for n = 1..20000

Wikipedia, Wilson's theorem

Example

For n = 26 it follows:
i = isqrt(26) = 5
(i-1)! = 24
(i-1)! = i-1 mod i
24 = 4 mod 5

Maple

seq(`if`(t=1 or isprime(t), seq(i, i=t^2..(t+1)^2-1), NULL), t=1..100); # Robert Israel, Jan 09 2016

Mathematica

Select[Range@ 181, Function[n, Mod[(# - 1)!, #] == # - 1 &@ IntegerPart@ Sqrt@ n]] (* Michael De Vlieger, Jan 09 2016 *)

Prog

(Sidef)
10000.times { |n|
    var i = n.isqrt;
    if ((i-1)! % i == i-1) {
        say n
    }
}
(PARI) lista(nn) = for(n=1, nn, if(Mod((sqrtint(n)-1)!, sqrtint(n)) == sqrtint(n)-1, print1(n, ", "))); \\ Altug Alkan, Jan 12 2016

Crossrefs

Cf. A000196, A000578.

Sequence in context: A084688 A194898 A331271 * A023769 A023796 A032950

Adjacent sequences: A267013 A267014 A267015 * A267017 A267018 A267019

Keyword

nonn,easy

Author

Daniel Suteu, Jan 08 2016

Status

approved