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

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

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^(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

Adjacent sequences: A217094 A217095 A217096 * A217098 A217099 A217100

Keyword

nonn,base

Author

Hieronymus Fischer, Feb 10 2013

Status

approved