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A348467
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The number of distinct decimal representations of integers embedded as slices in the decimal representation of n!.
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1
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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
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refs;
listen;
history;
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internal format)
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OFFSET
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0,5
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LINKS
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FORMULA
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EXAMPLE
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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.
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MATHEMATICA
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a[n_] := Length@ DeleteDuplicates[FromDigits /@ Rest@ Subsequences[ IntegerDigits[n!]]]; Array[a, 50, 0] (* Amiram Eldar, Oct 19 2021 *)
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PROG
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(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
(Python)
from math import factorial
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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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