A378188 Record values in A205561.

2, 3, 4, 5, 8, 10, 20, 22, 24, 29, 34, 36, 49, 59, 72, 76, 90, 108, 110, 144, 162, 173, 175, 189, 281, 410, 413, 473, 478, 511, 512, 513, 539, 555, 632, 639, 783, 790, 794, 820, 944, 1096, 1153, 1178, 1226, 1264, 1413, 1438, 1622, 1633, 1689, 1717, 1801, 1892, 1982, 2002, 2057, 2446, 2521, 2592

Offset: 1

Author

Robert Israel, Nov 19 2024

Keywords

• nonn

Comments

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'.

Examples

			a(5) = 8 is a term because A205561(13) = 8, but A205561(n) < 8 for all n < 13.
		

Links

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

Crossrefs

Cf. A205561, A378189.

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:
R:= 2: m:= 2: count:= 1:
for k from 2 while count < 70 do
  v:= f(k);
  if v > m then R:= R,v; count:= count+1; m:= v;
  fi
od:
R;