A378189 - OEIS

%I #7 Nov 21 2024 09:05:18

%S 1,3,5,7,13,17,37,83,137,173,193,269,311,479,607,673,1019,1427,1523,

%T 1613,3391,3527,4817,5021,5623,9887,14891,15823,21701,22727,24439,

%U 26399,27581,28771,29339,35491,37967,49207,51157,52639,54799,64303,93077,104323,115279,116981,117881,135209,157177

%N Positions of records in A205561.

%C 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 Robert Israel, <a href="/A378189/b378189.txt">Table of n, a(n) for n = 1..113</a>

%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 J:= 1: m:= 2: count:= 1:

%p for k from 2 while count < 70 do

%p   v:= f(k);

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

%p   fi

%p od:

%p J;

%Y Cf. A205561, A378188.

%K nonn

%O 1,2

%A _Robert Israel_, Nov 19 2024