A120004 Number of distinct numbers as substrings of n in decimal representation.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 4, 4, 5, 5, 5, 5

Offset: 0

Author

Reinhard Zumkeller, Jun 15 2006

Keywords

• nonn
• base

Comments

a(n) = A079790(n) for n <= 100;

a(A120005(n)) = n and a(m) < n for m < A120005(n).

a(n) = length of n-th row in A218978; see also A154771. - Reinhard Zumkeller, Nov 10 2012

Examples

			n=101: {'1','0','10','01','101'} -> a(101) = #{0,1,10,101} = 4;
n=102: {'1','0','2','10','02','102'} -> a(102) = #{0,1,2,10,102} = 5.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A119999.

Programs

Haskell

import Data.List (isInfixOf)
a120004 n = sum $ map (fromEnum . (`isInfixOf` show n) . show) [0..n]
-- Reinhard Zumkeller, Jul 16 2012, Aug 14 2011

Mathematica

a[n_] := Length@ DeleteDuplicates[FromDigits /@ Rest@ Subsequences[ IntegerDigits[n]]]; Array[a, 100, 0] (* Amiram Eldar, Oct 19 2021 *)

PARI

a(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); \\

Python

def A120004(n):
    s = str(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

Extensions

Offset changed and a(0)=1 inserted, in consequence of Zak Seidov's correction in A120005. - Reinhard Zumkeller, May 30 2010