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%I #9 Apr 01 2022 21:36:36
%S 1,3,6,7,13,15,25,26,28,31,49,53,59,63
%N Binary terms such that duplicating the rightmost bit and counting repeats gives a palindrome.
%C Decimal-binary representations of palindromic continued fractions.
%C Using the conversion rules, the first 14 fractions in the Stern-Brocot infinite Farey tree, (rational fractions k, 0 < k < 1) with palindromic continued fraction representations are: 1/2, 1/3, 2/5, 1/4, 3/8, 1/5, 5/12, 5/13, 3/10, 1/6, 7/16, 8/21, 4/15, 1/7.
%e The first 14 binary terms corresponding to (1, 3, 6, 7, ...) = 1, 11, 110, 111, 1101, 1111, 1101, 11010, 11100, 11111, 110001, 110101, 111011, 111111, ...). 26 in binary is 11010. Appending an 0 to the right gives 110100. Recording the number of repeats, we get 2,1,1,2, a palindrome, so 26 is in the sequence. Later, we can obtain the fraction corresponding to continued fraction [2,1,1,2] = 5/13.
%K nonn,base
%O 1,2
%A _Gary W. Adamson_, Jan 29 2008
%E Edited by _Franklin T. Adams-Watters_, Mar 29 2014
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