A342845 Number of distinct even numbers visible as proper substrings of n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 2, 3, 2, 3

Offset: 0

Author

Sean A. Irvine, Mar 24 2021

Keywords

• nonn
• base
• easy

Comments

Here substrings must be contiguous.

Examples

			a(10)=1 because we can form 0.
a(24)=2 because we can form 2, 4.
a(102)=3 because we can form 0, 2, 10.
a(124)=4 because we can form the following even numbers: 2, 4, 12, 24.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A045887, A045888, A342846.

Programs

Haskell

import Data.List (isInfixOf)
a045887 n = length $ filter (`isInfixOf` (show n)) $ map show [0, 2..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 "02468" and j-i < len(s): # even and proper substring
        eset.add(int(s[i:j]))
  return len(eset)
print([a(n) for n in range(105)]) # Michael S. Branicky, Mar 23 2021