A331804 - OEIS

%I #12 Jan 28 2020 01:36:53

%S 0,1,1,3,1,5,3,7,1,9,5,5,3,5,7,15,1,17,9,9,5,21,6,7,3,9,5,27,7,7,15,

%T 31,1,33,17,17,9,9,9,9,5,9,21,21,6,45,14,15,3,17,9,51,5,21,27,27,7,9,

%U 7,27,15,15,31,63,1,65,33,33,17,17,17,17,9,73,10,9

%N a(n) is the largest positive integer occurring, when written in binary, as a substring in both binary n and its reversal (A030101(n)).

%C We set a(0) = 0 by convention.

%C a(7479) = 29 ("11101" in binary) is the first term that does not belong to A057890.

%H Rémy Sigrist, <a href="/A331804/b331804.txt">Table of n, a(n) for n = 0..8192</a>

%F a(n) = A175466(n, A030101(n)) for any n > 0.

%F a(n) <= n with equality iff n is a binary palindrome (A006995).

%e The first terms, alongside the binary representations of n and of a(n), are:

%e   n   a(n)  bin(n)  bin(a(n))

%e   --  ----  ------  ---------

%e    0     0       0          0

%e    1     1       1          1

%e    2     1      10          1

%e    3     3      11         11

%e    4     1     100          1

%e    5     5     101        101

%e    6     3     110         11

%e    7     7     111        111

%e    8     1    1000          1

%e    9     9    1001       1001

%e   10     5    1010        101

%e   11     5    1011        101

%e   12     3    1100         11

%o (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 a(n) = my (i=setintersect(sub(n), sub(fromdigits(Vecrev(binary(n)),2)))); i[#i]

%Y Cf. A006995, A030101, A047813, A057890, A175466.

%K nonn,base

%O 0,4

%A _Rémy Sigrist_, Jan 26 2020