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A267016 Numbers that satisfy: (isqrt(n)-1)! = isqrt(n)-1 mod isqrt(n). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 8 05:22 EST 2022. Contains 358672 sequences. (Running on oeis4.)