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Greatest binary palindrome (cf. A006995) with n binary digits such that the number of contiguous palindromic bit patterns is minimal.
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%I #16 Jul 21 2015 11:15:11

%S 1,3,5,9,27,51,107,165,403,843,1675,2661,5709,13515,27083,39513,

%T 108235,208083,432843,682341,1664211,3461835,6922955,10918245,

%U 23434061,55390923,110785227,161912409,443134667,852178131,1772532427,2795133285,6817395923,14180201163,28360356555

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

%C Subsequence of A217099.

%C 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.

%H Hieronymus Fischer, <a href="/A217098/b217098.txt">Table of n, a(n) for n = 1..500</a>

%F 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)).

%F a(n) = A006995(j), where j := j(n) = max(k > A206915(2^(n-1)) | A206924(k) = min(A206925(A006995(i)) | i > A206915(2^(n-1)))).

%F a(n) = max(p | p is binary palindrome with n binary digits and A206925(p) = 2*(n-1) + floor((n-3)/2)).

%e 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.

%e 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.

%e 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.

%Y Cf. A006995, A206923, A206924, A206925, A206926, A070939, A217097, A217099, A217100, A217101.

%K nonn,base

%O 1,2

%A _Hieronymus Fischer_, Jan 23 2013