

A217098


Greatest binary palindrome (cf. A006995) with n binary digits such that the number of contiguous palindromic bit patterns is minimal.


2



1, 3, 5, 9, 27, 51, 107, 165, 403, 843, 1675, 2661, 5709, 13515, 27083, 39513, 108235, 208083, 432843, 682341, 1664211, 3461835, 6922955, 10918245, 23434061, 55390923, 110785227, 161912409, 443134667, 852178131, 1772532427, 2795133285, 6817395923, 14180201163, 28360356555
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OFFSET

1,2


COMMENTS

Subsequence of A217099.
a(n) is the greatest binary palindrome with n binary digits which meets the minimal possible number of palindromic substrings for that number of digits.


LINKS

Hieronymus Fischer, Table of n, a(n) for n = 1..500


FORMULA

a(n) = max(p  p is binary palindrome with n binary digits and A206925(p) = min(A206925(q)  q is binary palindrome with n binary digits)).
a(n) = A006995(j), where j := j(n) = max(k > A206915(2^(n1))  A206924(k) = min(A206925(A006995(i))  i > A206915(2^(n1)))).
a(n) = max(p  p is binary palindrome with n binary digits and A206925(p) = 2*(n1) + floor((n3)/2)).


EXAMPLE

a(1) = 1, since 1 is the largest binary palindrome with 1 palindromic substring (=1) which is the minimum for binary palindromes with 1 place.
a(3) = 5, since 5=101_2 is the largest binary palindrome with 4 palindromic substrings which is the minimum for binary palindromes with 3 places.
a(6) = 51, since 51=110011_2 is the largest binary palindrome with 11 palindromic substrings which is the minimum for binary palindromes with 6 places.


CROSSREFS

Cf. A006995, A206923, A206924, A206925, A206926, A070939, A217097, A217099, A217100, A217101.
Sequence in context: A171877 A004044 A192152 * A262314 A209286 A082711
Adjacent sequences: A217095 A217096 A217097 * A217099 A217100 A217101


KEYWORD

nonn,base


AUTHOR

Hieronymus Fischer, Jan 23 2013


STATUS

approved



