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

0,11

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

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A119999.

Sequence in context: A142246 A080428 A343886 * A079790 A098726 A065801

Adjacent sequences: A120001 A120002 A120003 * A120005 A120006 A120007

Keyword

nonn,base

Author

Reinhard Zumkeller, Jun 15 2006

Extensions

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

Status

approved