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A378189 Positions of records in A205561.

%I A378189 #7 Nov 21 2024 09:05:18
%S A378189 1,3,5,7,13,17,37,83,137,173,193,269,311,479,607,673,1019,1427,1523,
%T A378189 1613,3391,3527,4817,5021,5623,9887,14891,15823,21701,22727,24439,
%U A378189 26399,27581,28771,29339,35491,37967,49207,51157,52639,54799,64303,93077,104323,115279,116981,117881,135209,157177
%N A378189 Positions of records in A205561.
%C A378189 Numbers m such that there is k such that for every m' < m, there exist j and k' such that 1 <= j < k' <= k and m' divides (2*k')! - (2*j)!, but there do not exist j and k' such that 1 <= j < k' <= k and m divides (2*k')! - (2*j)!.
%H A378189 Robert Israel, <a href="/A378189/b378189.txt">Table of n, a(n) for n = 1..113</a>
%p A378189 f:= proc(n) local S, j, x;
%p A378189   S:= {}:
%p A378189   x:= 1:
%p A378189   for j from 1 do
%p A378189     x:=x*2*j*(2*j-1) mod n;
%p A378189     if member(x, S) then return j fi;
%p A378189     S:= S union {x}
%p A378189   od
%p A378189 end proc:
%p A378189 J:= 1: m:= 2: count:= 1:
%p A378189 for k from 2 while count < 70 do
%p A378189   v:= f(k);
%p A378189   if v > m then J:= J, k; count:= count+1; m:= v;
%p A378189   fi
%p A378189 od:
%p A378189 J;
%Y A378189 Cf. A205561, A378188.
%K A378189 nonn
%O A378189 1,2
%A A378189 _Robert Israel_, Nov 19 2024