A378188 - OEIS

%I #8 Nov 21 2024 09:05:14

%S 2,3,4,5,8,10,20,22,24,29,34,36,49,59,72,76,90,108,110,144,162,173,

%T 175,189,281,410,413,473,478,511,512,513,539,555,632,639,783,790,794,

%U 820,944,1096,1153,1178,1226,1264,1413,1438,1622,1633,1689,1717,1801,1892,1982,2002,2057,2446,2521,2592

%N Record values in A205561.

%C Numbers m such that there exist j and k such that 1 <= j < m and (2*m)! - (2*j)! is divisible by k, but for all m' < m there is no j' with 1 <= j' < m' and (2*m')! - (2*j')! divisible by k, and for all k' with 1 <= k' < k there exist j' and m' with 1 <= j' < m' < m and (2*m')! - (2*j')! divisible by k'.

%H Robert Israel, <a href="/A378188/b378188.txt">Table of n, a(n) for n = 1..113</a>

%e a(5) = 8 is a term because A205561(13) = 8 (as 8 divides (2*13)! -  but A205561(n) < 8 for all n < 13.

%p f:= proc(n) local S,j,x;

%p   S:= {}:

%p   x:= 1:

%p   for j from 1 do

%p     x:=x*2*j*(2*j-1) mod n;

%p     if member(x,S) then return j fi;

%p     S:= S union {x}

%p   od

%p end proc:

%p R:= 2: m:= 2: count:= 1:

%p for k from 2 while count < 70 do

%p   v:= f(k);

%p   if v > m then R:= R,v; count:= count+1; m:= v;

%p   fi

%p od:

%p R;

%Y Cf. A205561, A378189.

%K nonn

%O 1,1

%A _Robert Israel_, Nov 19 2024