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A254449 a(n) is the smallest nonnegative integer such that a(n)! contains a string of exactly n consecutive 4's.

%I A254449 #44 Mar 21 2019 02:40:11
%S A254449 0,4,21,63,117,375,1325,1253,5741,30455,83393,68094,565882,2666148,
%T A254449 1514639
%N A254449 a(n) is the smallest nonnegative integer such that a(n)! contains a string of exactly n consecutive 4's.
%C A254449 a(6) and a(7) are anagrams.
%e A254449 a(1) = 4 since 4! = 24 contains '4', and 4 is the smallest integer for which this condition is met.
%e A254449 a(2) = 21 since 21! = 51090942171709440000 contains '44'.
%t A254449 A254449[n_] := Module[{m = 0},
%t A254449    t = Table[4, n];
%t A254449    While[! MemberQ[Split[IntegerDigits[m!]], t], m++]; m];
%t A254449 Join[{0}, Table[A254449[n], {n, 1, 14}]] (* _Robert Price_, Mar 20 2019 *)
%o A254449 (Python)
%o A254449 def A254449(n):
%o A254449     if n == 0:
%o A254449         return 0
%o A254449     i, m, s = 1, 1, '4'*n
%o A254449     s2 = s+'4'
%o A254449     while True:
%o A254449         m *= i
%o A254449         sn = str(m)
%o A254449         if s in sn and s2 not in sn:
%o A254449             return i
%o A254449         i += 1 # _Chai Wah Wu_, Dec 29 2015
%Y A254449 Cf. A254042, A254447, A254448, A254500, A254501, A254502, A254716, A254717, A252652.
%K A254449 nonn,more,base
%O A254449 0,2
%A A254449 _Martin Y. Champel_, Jan 30 2015
%E A254449 a(12) from _Jon E. Schoenfield_, Feb 27 2015
%E A254449 a(0) prepended by _Jon E. Schoenfield_, Mar 01 2015
%E A254449 a(14) by _Lars Blomberg_, Mar 19 2015
%E A254449 a(13) by _Bert Dobbelaere_, Oct 29 2018