cp's OEIS Frontend

A045887 Number of distinct even numbers visible as proper subsequences of n.

%I A045887 #26 Mar 24 2021 22:15:20
%S A045887 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,
%T A045887 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,
%U A045887 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
%N A045887 Number of distinct even numbers visible as proper subsequences of n.
%H A045887 Sean A. Irvine, <a href="/A045887/b045887.txt">Table of n, a(n) for n = 0..10000</a>
%H A045887 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a045/A045887.java">Java program</a> (github)
%e A045887 a(10)=1 because we can form 0.
%e A045887 a(24)=2 because we can form 2, 4.
%e A045887 a(102)=4 because we can form 0, 2, 10, 12.
%e A045887 a(124)=5 because we can form the following even numbers: 2, 4, 12, 14, 24.
%o A045887 (Python)
%o A045887 from itertools import combinations
%o A045887 def a(n):
%o A045887   s, eset = str(n), set()
%o A045887   for i in range(len(s)):
%o A045887     for j in range(i+1, len(s)+1):
%o A045887       if s[j-1] in "02468":
%o A045887         if len(s[i:j]) <= 2 and j-i < len(s):
%o A045887           eset.add(int(s[i:j]))
%o A045887         else:
%o A045887           middle = s[i+1:j-1]
%o A045887           for k in range(len(middle)+1):
%o A045887             for c in combinations(middle, k):
%o A045887               t = s[i] + "".join(c) + s[j-1]
%o A045887               if len(t) < len(s):
%o A045887                 eset.add(int(t))
%o A045887   return len(eset)
%o A045887 print([a(n) for n in range(105)]) # _Michael S. Branicky_, Mar 24 2021
%Y A045887 Cf. A045888, A342845, A342846.
%K A045887 base,easy,nonn
%O A045887 0,21
%A A045887 _Felice Russo_
%E A045887 More terms from _Fabian Rothelius_, Feb 08 2001
%E A045887 a(102) and a(104) corrected by _Reinhard Zumkeller_, Jul 19 2011
%E A045887 a(102) and a(104) reverted to original values by _Sean A. Irvine_, Mar 23 2021