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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
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
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^(n-1)) | A206924(k) = min(A206925(A006995(i)) | i > A206915(2^(n-1)))).
a(n) = min(p | p is binary palindrome with n binary digits and A206925(p) = 2*(n-1) + floor((n-3)/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: A337780 A178717 A006723 * A298590 A262451 A096390
KEYWORD
nonn,base
AUTHOR
Hieronymus Fischer, Feb 10 2013
STATUS
approved