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

1,13

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

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..20000

Sean A. Irvine, Java program (github)

Example

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.

Prog

(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

Crossrefs

Cf. A045887, A045888, A342845.

Sequence in context: A167404 A280223 A062754 * A045888 A335885 A335875

Adjacent sequences: A342843 A342844 A342845 * A342847 A342848 A342849

Keyword

nonn,base,easy

Author

Sean A. Irvine, Mar 24 2021

Status

approved