

A217097


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


2



0, 3, 5, 9, 17, 45, 73, 153, 297, 717, 1241, 2409, 4841, 13011, 21349, 38505, 76905, 183117, 307817, 632409, 1231465, 2929485, 5060185, 9853545, 19708521, 53261523, 87349605, 157653609, 315300457, 749917005, 1261214313, 2590611033, 5044869737, 11998647117, 20724946521
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OFFSET

1,2


COMMENTS

Subsequence of A217099.
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.


LINKS

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


FORMULA

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


EXAMPLE

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.
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.
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.


CROSSREFS

Cf. A006995, A206923, A206924, A206925, A206926, A070939, A217098, 217099, 217100, 217101.
Sequence in context: A297011 A178717 A006723 * A298590 A262451 A096390
Adjacent sequences: A217094 A217095 A217096 * A217098 A217099 A217100


KEYWORD

nonn,base


AUTHOR

Hieronymus Fischer, Feb 10 2013


STATUS

approved



