A378189 Positions of records in A205561.

1, 3, 5, 7, 13, 17, 37, 83, 137, 173, 193, 269, 311, 479, 607, 673, 1019, 1427, 1523, 1613, 3391, 3527, 4817, 5021, 5623, 9887, 14891, 15823, 21701, 22727, 24439, 26399, 27581, 28771, 29339, 35491, 37967, 49207, 51157, 52639, 54799, 64303, 93077, 104323, 115279, 116981, 117881, 135209, 157177

Offset: 1

Author

Robert Israel, Nov 19 2024

Keywords

• nonn

Comments

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)!.

Links

• Robert Israel, Table of n, a(n) for n = 1..113

Crossrefs

Cf. A205561, A378188.

Programs

Maple

f:= proc(n) local S, j, x;
  S:= {}:
  x:= 1:
  for j from 1 do
    x:=x*2*j*(2*j-1) mod n;
    if member(x, S) then return j fi;
    S:= S union {x}
  od
end proc:
J:= 1: m:= 2: count:= 1:
for k from 2 while count < 70 do
  v:= f(k);
  if v > m then J:= J, k; count:= count+1; m:= v;
  fi
od:
J;