A342846 Number of distinct odd numbers visible as proper substrings of n.

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, 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, 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

Offset: 1

Author

Sean A. Irvine, Mar 24 2021

Keywords

• nonn
• base
• easy

Comments

Here substrings are contiguous.

a(A164766(n)) = n and a(m) <> n for m < A164766(n); a(A014263(n)) = 0. - Reinhard Zumkeller, Aug 25 2009

Examples

			a(10)=1 since we can see 1 as a proper substring of 10.
a(105)=2 since we can see 1, 5.
a(132)=3 because we can see 1, 3, 13.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..20000
• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A045887, A045888, A342845.

Programs

Haskell

import Data.List (isInfixOf)
a045888 n = length $ filter (`isInfixOf` (show n)) $ map show [1, 3..n-1]
-- Reinhard Zumkeller, Jul 19 2011

Python

def a(n):
  s, eset = str(n), set()
  for i in range(len(s)):
    for j in range(i+1, len(s)+1):
      if s[j-1] in "13579" and j-i < len(s): # odd and proper substring
        eset.add(int(s[i:j]))
  return len(eset)
print([a(n) for n in range(1, 105)]) # Michael S. Branicky, Mar 24 2021