A293246 a(n) is the smallest k > 1 such that A000166(k) is divisible by n!.

2, 2, 3, 7, 25, 121, 241, 1681, 13441, 40321, 403201, 2016001, 3225601, 41932801, 609638401

Offset

0,1

Comments

a(n) is the smallest k > 1 such that round(k!/e) is divisible by n!.

Terms are 0! + 1, 1! + 1, 2! + 1, 3! + 1, 4! + 1, 5! + 1, 6!/3 + 1, 7!/3 + 1, ...

Links

Table of n, a(n) for n=0..14.

Example

a(3) = 7 because the smallest nonzero subfactorial number that is divisible by 3! is A000166(7) = 1854.

Maple

f:= proc(n) local k, t, p;
p:= n!;
t:= 0;
for k from 2 do
  t:= k*t + (-1)^k mod p;
  if t = 0 then return k fi
od:
end proc:
seq(f(n), n=0..13); # Robert Israel, Oct 03 2017

Crossrefs

Cf. A000142, A000166.

Sequence in context: A083701 A076996 A139148 * A185387 A038507 A077001

Adjacent sequences: A293243 A293244 A293245 * A293247 A293248 A293249

Keyword

nonn,more

Author

Altug Alkan, Oct 03 2017

Extensions

a(8)-a(14) from Robert Israel, Oct 03 2017

Status

approved