STATUS
reviewed
approved
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Revision History for A331804
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a(n) is the largest positive integer occurring, when written in binary, as a substring in both binary n and its reversal (A030101(n)).
(history; published version)
(history; published version)
STATUS
proposed
reviewed
STATUS
editing
proposed
LINKS
Rémy Sigrist, <a href="/A331804/b331804.txt">Table of n, a(n) for n = 0..8192</a>
STATUS
approved
editing
STATUS
proposed
approved
STATUS
editing
proposed
NAME
a(n) is the largest positive integer occurring, when written in binary, as a substring in both binary n and in the binary its reversal of n (A030101(n)).
FORMULA
a(n) <= n with equality iff n is a binary palindrome (A006995).
EXAMPLE
The first terms, alongside the binary representations of n and of a(n), are:
n a(n) bin(n) bin(a(n))
-- ---- ------ ---------
0 0 0 0
1 1 1 1
2 1 10 1
3 3 11 11
4 1 100 1
5 5 101 101
6 3 110 11
7 7 111 111
8 1 1000 1
9 9 1001 1001
10 5 1010 101
11 5 1011 101
12 3 1100 11
PROG
(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) }
a(n) = my (i=setintersect(sub(n), sub(fromdigits(Vecrev(binary(n)), 2)))); i[#i]
COMMENTS
All terms a(7479) = 29 ("11101" in binary) is the first term that does not belong to A057890.