cp's OEIS Frontend

A331804 a(n) is the largest positive integer occurring, when written in binary, as a substring in both binary n and its reversal (A030101(n)).

%I A331804 #12 Jan 28 2020 01:36:53
%S A331804 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 A331804 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 A331804 7,27,15,15,31,63,1,65,33,33,17,17,17,17,9,73,10,9
%N A331804 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 A331804 We set a(0) = 0 by convention.
%C A331804 a(7479) = 29 ("11101" in binary) is the first term that does not belong to A057890.
%H A331804 Rémy Sigrist, <a href="/A331804/b331804.txt">Table of n, a(n) for n = 0..8192</a>
%F A331804 a(n) = A175466(n, A030101(n)) for any n > 0.
%F A331804 a(n) <= n with equality iff n is a binary palindrome (A006995).
%e A331804 The first terms, alongside the binary representations of n and of a(n), are:
%e A331804   n   a(n)  bin(n)  bin(a(n))
%e A331804   --  ----  ------  ---------
%e A331804    0     0       0          0
%e A331804    1     1       1          1
%e A331804    2     1      10          1
%e A331804    3     3      11         11
%e A331804    4     1     100          1
%e A331804    5     5     101        101
%e A331804    6     3     110         11
%e A331804    7     7     111        111
%e A331804    8     1    1000          1
%e A331804    9     9    1001       1001
%e A331804   10     5    1010        101
%e A331804   11     5    1011        101
%e A331804   12     3    1100         11
%o A331804 (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 A331804 a(n) = my (i=setintersect(sub(n), sub(fromdigits(Vecrev(binary(n)),2)))); i[#i]
%Y A331804 Cf. A006995, A030101, A047813, A057890, A175466.
%K A331804 nonn,base
%O A331804 0,4
%A A331804 _Rémy Sigrist_, Jan 26 2020