A254501 a(n) is the smallest nonnegative integer such that a(n)! contains a string of exactly n consecutive 6's.
0, 3, 20, 38, 35, 213, 1122, 3415, 10214, 32430, 145197, 351679, 666779, 813843, 3765934
Offset: 0
Examples
a(1) = 3 since 3! equals 6 and contains '6'. a(2) = 20 since 20! contains '66' and 20 is the smallest integer for which the condition is met.
Programs
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Mathematica
A254451[n_] := Module[{m = 0}, If[n == 0, While[MemberQ[IntegerDigits[m!], 6], m++]; m, t = Table[6, n]; While[! MemberQ[Split[IntegerDigits[m!]], t], m++]; m]]; Table[A254451[n], {n, 0, 7}] (* Robert Price, Mar 21 2019 *)
Extensions
a(10), a(11) from Jon E. Schoenfield, Feb 21 2015, Feb 23 2015
a(0) prepended by Jon E. Schoenfield, Mar 01 2015
a(12), a(13) from Jon E. Schoenfield, Mar 07 2015, Mar 10 2015
a(14) from Bert Dobbelaere, Oct 29 2018