A348467 The number of distinct decimal representations of integers embedded as slices in the decimal representation of n!.

1, 1, 1, 1, 3, 6, 6, 7, 11, 20, 25, 33, 32, 41, 60, 72, 80, 106, 104, 132, 140, 150, 173, 239, 241, 269, 306, 344, 369, 440, 487, 542, 550, 639, 639, 754, 799, 840, 777, 932, 1094, 1032, 1129, 1203, 1376, 1440, 1386, 1681, 1700, 1737, 1700, 1948, 1964, 2099, 2219

Offset

0,5

Links

Table of n, a(n) for n=0..54.

Formula

a(n) = A120004(n!). - Michel Marcus, Oct 19 2021

Example

0:  1 // 1;
1:  1 // 1;
2:  1 // 2;
3:  1 // 6;
4:  3 // 2,4,24;
5:  6 // 0,1,2,12,20,120;
6:  6 // 0,2,7,20,72,720;
7:  7 // 0,4,5,40,50,504,5040;
8: 11 // 0,2,3,4,20,32,40,320,403,4032,40320;
9: 20 // 0,2,3,6,8,28,36,62,80,88,288,362,628,880,2880,3628,6288,36288,62880, 362880.

Mathematica

a[n_] := Length@ DeleteDuplicates[FromDigits /@ Rest@ Subsequences[ IntegerDigits[n!]]]; Array[a, 50, 0] (* Amiram Eldar, Oct 19 2021 *)

Prog

(PARI) f(n) = if (n==0, return (1)); my(d=digits(n), list=List()); for (k=1, #d, for (j=1, #d-k+1, my(dk=vector(j, i, d[k+i-1])); listput(list, fromdigits(dk)); ); ); #Set(list); \\ A120004
a(n) = f(n!); \\ Michel Marcus, Oct 19 2021
(Python)
from math import factorial
def A348467(n):
    s = str(factorial(n))
    m = len(s)
    return len(set(int(s[i:j]) for i in range(m) for j in range(i+1, m+1))) # Chai Wah Wu, Oct 19 2021

Crossrefs

Cf. A120004, A219032, A000142.

Sequence in context: A239318 A177783 A228945 * A178746 A229986 A025500

Adjacent sequences: A348464 A348465 A348466 * A348468 A348469 A348470

Keyword

nonn,base

Author

Peter Luschny, Oct 19 2021

Status

approved