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A378188 Record values in A205561.

%I A378188 #11 Mar 31 2025 01:47:06
%S A378188 2,3,4,5,8,10,20,22,24,29,34,36,49,59,72,76,90,108,110,144,162,173,
%T A378188 175,189,281,410,413,473,478,511,512,513,539,555,632,639,783,790,794,
%U A378188 820,944,1096,1153,1178,1226,1264,1413,1438,1622,1633,1689,1717,1801,1892,1982,2002,2057,2446,2521,2592
%N A378188 Record values in A205561.
%C A378188 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 A378188 Robert Israel, <a href="/A378188/b378188.txt">Table of n, a(n) for n = 1..113</a>
%e A378188 a(5) = 8 is a term because A205561(13) = 8, but A205561(n) < 8 for all n < 13.
%p A378188 f:= proc(n) local S,j,x;
%p A378188   S:= {}:
%p A378188   x:= 1:
%p A378188   for j from 1 do
%p A378188     x:=x*2*j*(2*j-1) mod n;
%p A378188     if member(x,S) then return j fi;
%p A378188     S:= S union {x}
%p A378188   od
%p A378188 end proc:
%p A378188 R:= 2: m:= 2: count:= 1:
%p A378188 for k from 2 while count < 70 do
%p A378188   v:= f(k);
%p A378188   if v > m then R:= R,v; count:= count+1; m:= v;
%p A378188   fi
%p A378188 od:
%p A378188 R;
%Y A378188 Cf. A205561, A378189.
%K A378188 nonn
%O A378188 1,1
%A A378188 _Robert Israel_, Nov 19 2024