A342846 - OEIS

%I #10 Mar 26 2021 06:32:57

%S 0,0,0,0,0,0,0,0,0,1,1,1,2,1,2,1,2,1,2,0,1,0,1,0,1,0,1,0,1,1,2,1,1,1,

%T 2,1,2,1,2,0,1,0,1,0,1,0,1,0,1,1,2,1,2,1,1,1,2,1,2,0,1,0,1,0,1,0,1,0,

%U 1,1,2,1,2,1,2,1,1,1,2,0,1,0,1,0,1,0,1,0,1,1,2,1,2,1,2,1,2,1,1,1,1,1,2,1,2

%N Number of distinct odd numbers visible as proper substrings of n.

%C Here substrings are contiguous.

%C a(A164766(n)) = n and a(m) <> n for m < A164766(n); a(A014263(n)) = 0. - _Reinhard Zumkeller_, Aug 25 2009

%H Reinhard Zumkeller, <a href="/A342846/b342846.txt">Table of n, a(n) for n = 1..20000</a>

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a342/A342846.java">Java program</a> (github)

%e a(10)=1 since we can see 1 as a proper substring of 10.

%e a(105)=2 since we can see 1, 5.

%e a(132)=3 because we can see 1, 3, 13.

%o (Haskell)

%o import Data.List (isInfixOf)

%o a045888 n = length $ filter (`isInfixOf` (show n)) $ map show [1, 3..n-1]

%o -- Reinhard Zumkeller, Jul 19 2011

%o (Python)

%o def a(n):

%o   s, eset = str(n), set()

%o   for i in range(len(s)):

%o     for j in range(i+1, len(s)+1):

%o       if s[j-1] in "13579" and j-i < len(s): # odd and proper substring

%o         eset.add(int(s[i:j]))

%o   return len(eset)

%o print([a(n) for n in range(1, 105)]) # _Michael S. Branicky_, Mar 24 2021

%Y Cf. A045887, A045888, A342845.

%K nonn,base,easy

%O 1,13

%A _Sean A. Irvine_, Mar 24 2021