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%I #20 Feb 13 2016 17:17:33
%S 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,
%T 49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,121,122,123,124,125,126,
%U 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
%N Numbers that satisfy: (isqrt(n)-1)! = isqrt(n)-1 mod isqrt(n).
%C Numbers n such that A000196(n) is in A008578 (i.e. is either 1 or prime). - _Robert Israel_, Jan 09 2016
%H Daniel Suteu, <a href="/A267016/b267016.txt">Table of n, a(n) for n = 1..20000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Wilson's_theorem">Wilson's theorem</a>
%e For n = 26 it follows:
%e i = isqrt(26) = 5
%e (i-1)! = 24
%e (i-1)! = i-1 mod i
%e 24 = 4 mod 5
%p 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
%t Select[Range@ 181, Function[n, Mod[(# - 1)!, #] == # - 1 &@ IntegerPart@ Sqrt@ n]] (* _Michael De Vlieger_, Jan 09 2016 *)
%o (Sidef)
%o 10000.times { |n|
%o var i = n.isqrt;
%o if ((i-1)! % i == i-1) {
%o say n
%o }
%o }
%o (PARI) lista(nn) = for(n=1, nn,if(Mod((sqrtint(n)-1)!, sqrtint(n)) == sqrtint(n)-1, print1(n, ", "))); \\ _Altug Alkan_, Jan 12 2016
%Y Cf. A000196, A000578.
%K nonn,easy
%O 1,2
%A _Daniel Suteu_, Jan 08 2016
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