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%I #7 Jul 11 2015 00:55:39
%S 22,30,10,4,6,2,1,132,314,403,259,2048,-1,-1,-1,-1
%N Smallest number whose base-2 Reverse and Add! trajectory (presumably) contains exactly n base-2 palindromes, or -1 if there is no such number.
%C Conjecture 1: For each k > 0 the trajectory of k eventually leads to a term in the trajectory of some j which belongs to A075252, i.e., whose trajectory (presumably) never leads to a palindrome. Conjecture 2: There is no k > 0 such that the trajectory of k contains more than eleven base 2 palindromes, i.e., a(n) = -1 for n > 11.
%C Base-2 analog of A077594 (base 10) and A091680 (base 4).
%H <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>
%e a(4) = 6 since the trajectory of 6 contains the four palindromes 9, 27, 255, 765 (1001, 11011, 11111111, 1011111101 in base 2) and at 48960 joins the trajectory of 22 = A075252(1) and the trajectories of 1 (A035522), 2, 3, 4, 5 contain resp. 6, 5, 5, 3, 3 palindromes.
%Y Cf. A035522, A006995, A075252, A077594, A091680.
%K sign,base
%O 0,1
%A _Klaus Brockhaus_, Feb 25 2004