cp's OEIS Frontend

A217097 Least binary palindrome (cf. A006995) with n binary digits such that the number of contiguous palindromic bit patterns is minimal.

%I A217097 #10 Jan 29 2016 11:13:55
%S A217097 0,3,5,9,17,45,73,153,297,717,1241,2409,4841,13011,21349,38505,76905,
%T A217097 183117,307817,632409,1231465,2929485,5060185,9853545,19708521,
%U A217097 53261523,87349605,157653609,315300457,749917005,1261214313,2590611033,5044869737,11998647117,20724946521
%N A217097 Least binary palindrome (cf. A006995) with n binary digits such that the number of contiguous palindromic bit patterns is minimal.
%C A217097 Subsequence of A217099.
%C A217097 a(n) is the least binary palindrome with n binary digits which meets the minimal possible number of palindromic substrings for that number of digits.
%H A217097 Hieronymus Fischer, <a href="/A217097/b217097.txt">Table of n, a(n) for n = 1..500</a>
%F A217097 a(n) = min(p | p is binary palindrome with n binary digits and A206925(p) = min(A206925(q) | q is binary palindrome with n binary digits)).
%F A217097 a(n) = A006995(j), where j := j(n) = min(k > A206915(2^(n-1)) | A206924(k) = min(A206925(A006995(i)) | i > A206915(2^(n-1)))).
%F A217097 a(n) = min(p | p is binary palindrome with n binary digits and A206925(p) = 2*(n-1) + floor((n-3)/2)).
%e A217097 a(1) = 0, since 0 is the least binary palindrome with 1 palindromic substring (=0) which is the minimum for binary palindromes with 1 place.
%e A217097 a(3) = 5, since 5=101_2 is the least binary palindrome with 4 palindromic substrings which is the minimum for binary palindromes with 3 places.
%e A217097 a(6) = 45, since 45=101101_2 is the least binary palindrome with 11 palindromic substrings which is the minimum for binary palindromes with 6 places.
%Y A217097 Cf. A006995, A206923, A206924, A206925, A206926, A070939, A217098, 217099, 217100, 217101.
%K A217097 nonn,base
%O A217097 1,2
%A A217097 _Hieronymus Fischer_, Feb 10 2013