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

0,21

Comments

Here substrings must be contiguous.

Links

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

Sean A. Irvine, Java program (github)

Example

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.

Prog

(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

Crossrefs

Cf. A045887, A045888, A342846.

Sequence in context: A276172 A322028 A079806 * A045887 A056832 A105931

Adjacent sequences: A342842 A342843 A342844 * A342846 A342847 A342848

Keyword

nonn,base,easy

Author

Sean A. Irvine, Mar 24 2021

Status

approved