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

0, 4, 21, 63, 117, 375, 1325, 1253, 5741, 30455, 83393, 68094, 565882, 2666148, 1514639

Offset: 0

Author

Martin Y. Champel, Jan 30 2015

Keywords

• nonn
• more
• base

Comments

a(6) and a(7) are anagrams.

Examples

			a(1) = 4 since 4! = 24 contains '4', and 4 is the smallest integer for which this condition is met.
a(2) = 21 since 21! = 51090942171709440000 contains '44'.
		

Crossrefs

Cf. A254042, A254447, A254448, A254500, A254501, A254502, A254716, A254717, A252652.

Programs

Mathematica

A254449[n_] := Module[{m = 0},
   t = Table[4, n];
   While[! MemberQ[Split[IntegerDigits[m!]], t], m++]; m];
Join[{0}, Table[A254449[n], {n, 1, 14}]] (* Robert Price, Mar 20 2019 *)

Python

def A254449(n):
    if n == 0:
        return 0
    i, m, s = 1, 1, '4'*n
    s2 = s+'4'
    while True:
        m *= i
        sn = str(m)
        if s in sn and s2 not in sn:
            return i
        i += 1 # Chai Wah Wu, Dec 29 2015

Extensions

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

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

a(14) by Lars Blomberg, Mar 19 2015

a(13) by Bert Dobbelaere, Oct 29 2018