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A217098 Greatest binary palindrome (cf. A006995) with n binary digits such that the number of contiguous palindromic bit patterns is minimal.

%I A217098 #16 Jul 21 2015 11:15:11
%S A217098 1,3,5,9,27,51,107,165,403,843,1675,2661,5709,13515,27083,39513,
%T A217098 108235,208083,432843,682341,1664211,3461835,6922955,10918245,
%U A217098 23434061,55390923,110785227,161912409,443134667,852178131,1772532427,2795133285,6817395923,14180201163,28360356555
%N A217098 Greatest binary palindrome (cf. A006995) with n binary digits such that the number of contiguous palindromic bit patterns is minimal.
%C A217098 Subsequence of A217099.
%C A217098 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 A217098 Hieronymus Fischer, <a href="/A217098/b217098.txt">Table of n, a(n) for n = 1..500</a>
%F A217098 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 A217098 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 A217098 a(n) = max(p | p is binary palindrome with n binary digits and A206925(p) = 2*(n-1) + floor((n-3)/2)).
%e A217098 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 A217098 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 A217098 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 A217098 Cf. A006995, A206923, A206924, A206925, A206926, A070939, A217097, A217099, A217100, A217101.
%K A217098 nonn,base
%O A217098 1,2
%A A217098 _Hieronymus Fischer_, Jan 23 2013