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A254448 a(n) is the smallest nonnegative integer such that a(n)! contains a string of exactly n consecutive 3's.

%I A254448 #38 Mar 21 2019 04:20:36
%S A254448 0,8,24,25,134,407,151,2936,8040,26808,49668,115189,429335,1365981,
%T A254448 3507499
%N A254448 a(n) is the smallest nonnegative integer such that a(n)! contains a string of exactly n consecutive 3's.
%e A254448 a(1) = 8 since 8! = 40320, which contains '3' and 8 is the smallest integer for which the condition is met.
%e A254448 a(2) = 24 since 24! = 620448401733239439360000 contains '33'.
%t A254448 A254448[n_] := Module[{m = 0},
%t A254448    If[n == 0, While[MemberQ[IntegerDigits[m!], 3], m++]; m,
%t A254448     t = Table[3, n];
%t A254448     While[! MemberQ[Split[IntegerDigits[m!]], t], m++]; m]];
%t A254448 Table[A254448[n], {n, 0, 14}] (* _Robert Price_, Mar 20 2019 *)
%Y A254448 Cf. A254042, A254447, A254449, A254500, A254501, A254502, A254716, A254717.
%K A254448 nonn,base
%O A254448 0,2
%A A254448 _Martin Y. Champel_, Jan 30 2015
%E A254448 a(11), a(12) from _Jon E. Schoenfield_, Feb 20 2015, Feb 24 2015
%E A254448 a(0) prepended by _Jon E. Schoenfield_, Mar 01 2015
%E A254448 a(13) from _Lars Blomberg_, Mar 19 2015
%E A254448 a(14) from _Bert Dobbelaere_, Oct 29 2018