A254447 a(n) is the smallest nonnegative integer such that a(n)! contains a string of exactly n consecutive 2's.

0, 2, 13, 31, 45, 200, 854, 3358, 4698, 29324, 55295, 263489, 567993, 2328803

Offset: 0

Author

Martin Y. Champel, Jan 30 2015

Keywords

• nonn
• base
• more

Comments

a(n) > 10^7 for n >= 14. - Bert Dobbelaere, Oct 29 2018

Examples

			a(0) = 0 since 0! equals 1, which does not contain any '2'.
For n = 1, a(1) = 2 as 2! = 2 contains '2'.
For n = 2, a(2) = 13 as 13! = 6227020800 contains '22' and 13 is the smallest integer for which the condition is met.
		

Crossrefs

Cf. A254042, A254448, A254449, A254500, A254501, A254502, A254716, A254717.

Programs

Mathematica

A254447[n_] := Module[{m = 0},
   If[n == 0, While[MemberQ[IntegerDigits[m!], 2], m++]; m,
    t = Table[2, n];
    While[! MemberQ[Split[IntegerDigits[m!]], t], m++]; m]];
Table[A254447[n], {n, 0, 13}](* Robert Price, Mar 20 2019 *)

Extensions

a(11), a(12) from Jon E. Schoenfield, Feb 22 2015, Feb 27 2015

a(0) prepended by Jon E. Schoenfield, Mar 01 2015

a(13) from Bert Dobbelaere, Oct 29 2018