A045887 Number of distinct even numbers visible as proper subsequences 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, 4, 2, 4

Offset

0,21

Links

Sean A. Irvine, 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)=4 because we can form 0, 2, 10, 12.
a(124)=5 because we can form the following even numbers: 2, 4, 12, 14, 24.

Prog

(Python)
from itertools import combinations
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":
        if len(s[i:j]) <= 2 and j-i < len(s):
          eset.add(int(s[i:j]))
        else:
          middle = s[i+1:j-1]
          for k in range(len(middle)+1):
            for c in combinations(middle, k):
              t = s[i] + "".join(c) + s[j-1]
              if len(t) < len(s):
                eset.add(int(t))
  return len(eset)
print([a(n) for n in range(105)]) # Michael S. Branicky, Mar 24 2021

Crossrefs

Cf. A045888, A342845, A342846.

Sequence in context: A322028 A079806 A342845 * A056832 A105931 A349163

Adjacent sequences: A045884 A045885 A045886 * A045888 A045889 A045890

Keyword

base,easy,nonn

Author

Felice Russo

Extensions

More terms from Fabian Rothelius, Feb 08 2001

a(102) and a(104) corrected by Reinhard Zumkeller, Jul 19 2011

a(102) and a(104) reverted to original values by Sean A. Irvine, Mar 23 2021

Status

approved