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

1,1

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'.

Links

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

Example

a(5) = 8 is a term because A205561(13) = 8 (as 8 divides (2*13)! -  but A205561(n) < 8 for all n < 13.

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;

Crossrefs

Cf. A205561, A378189.

Sequence in context: A222297 A211981 A019997 * A263875 A351702 A125157

Adjacent sequences: A378185 A378186 A378187 * A378189 A378190 A378191

Keyword

nonn

Author

Robert Israel, Nov 19 2024

Status

approved