cp's OEIS Frontend

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

%I A120004 #30 Oct 19 2021 13:22:52
%S A120004 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,
%T A120004 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,
%U A120004 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
%N A120004 Number of distinct numbers as substrings of n in decimal representation.
%C A120004 a(n) = A079790(n) for n <= 100;
%C A120004 a(A120005(n)) = n and a(m) < n for m < A120005(n).
%C A120004 a(n) = length of n-th row in A218978; see also A154771. - _Reinhard Zumkeller_, Nov 10 2012
%H A120004 Reinhard Zumkeller, <a href="/A120004/b120004.txt">Table of n, a(n) for n = 0..10000</a>
%e A120004 n=101: {'1','0','10','01','101'} -> a(101) = #{0,1,10,101} = 4;
%e A120004 n=102: {'1','0','2','10','02','102'} -> a(102) = #{0,1,2,10,102} = 5.
%t A120004 a[n_] := Length@ DeleteDuplicates[FromDigits /@ Rest@ Subsequences[ IntegerDigits[n]]]; Array[a, 100, 0] (* _Amiram Eldar_, Oct 19 2021 *)
%o A120004 (Haskell)
%o A120004 import Data.List (isInfixOf)
%o A120004 a120004 n = sum $ map (fromEnum . (`isInfixOf` show n) . show) [0..n]
%o A120004 -- _Reinhard Zumkeller_, Jul 16 2012, Aug 14 2011
%o A120004 (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); \\
%o A120004 (Python)
%o A120004 def A120004(n):
%o A120004     s = str(n)
%o A120004     m = len(s)
%o A120004     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
%Y A120004 Cf. A119999.
%K A120004 nonn,base
%O A120004 0,11
%A A120004 _Reinhard Zumkeller_, Jun 15 2006
%E A120004 Offset changed and a(0)=1 inserted, in consequence of Zak Seidov's correction in A120005. - _Reinhard Zumkeller_, May 30 2010