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A331803 a(n) is the largest positive integer occurring, when written in binary, as a substring in both binary n and binary n+1.

%I A331803 #9 Jan 28 2020 01:36:57
%S A331803 0,1,1,1,2,2,3,1,4,2,5,3,6,6,7,1,8,4,9,4,10,5,11,3,12,6,13,6,14,14,15,
%T A331803 1,16,8,17,4,18,9,19,4,20,10,21,11,22,11,23,3,24,12,25,6,26,13,27,7,
%U A331803 28,14,29,14,30,30,31,1,32,16,33,8,34,17,35,8,36,18
%N A331803 a(n) is the largest positive integer occurring, when written in binary, as a substring in both binary n and binary n+1.
%C A331803 We set a(0) = 0 by convention.
%H A331803 Rémy Sigrist, <a href="/A331803/b331803.txt">Table of n, a(n) for n = 0..8192</a>
%F A331803 a(n) = A175466(n, n+1) for any n > 0.
%F A331803 a(2*n) = n.
%F A331803 a(2^k-1) = 1 for any k > 0.
%e A331803 The first terms, alongside the binary representations of n, n+1 and a(n), are:
%e A331803   n   a(n)  bin(n)  bin(n+1)  bin(a(n))
%e A331803   --  ----  ------  --------  ---------
%e A331803    0     0       0         1          0
%e A331803    1     1       1        10          1
%e A331803    2     1      10        11          1
%e A331803    3     1      11       100          1
%e A331803    4     2     100       101         10
%e A331803    5     2     101       110         10
%e A331803    6     3     110       111         11
%e A331803    7     1     111      1000          1
%e A331803    8     4    1000      1001        100
%e A331803    9     2    1001      1010         10
%e A331803   10     5    1010      1011        101
%o A331803 (PARI) sub(n) = { my (b=binary(n), s=[0]); for (i=1, #b, if (b[i], for (j=i, #b, s=setunion(s, Set(fromdigits(b[i..j], 2)))))); return (s) }
%o A331803 a(n) = my (i=setintersect(sub(n), sub(n+1))); i[#i]
%Y A331803 Cf. A175466.
%K A331803 nonn,base
%O A331803 0,5
%A A331803 _Rémy Sigrist_, Jan 26 2020