A091680 - OEIS

%I #10 Jul 11 2015 00:52:42

%S 290,78,18,6,3,36,21,19,7,8,4,2,1,-1,-1,-1,-1,-1,-1,-1,-1

%N Smallest number whose base-4 Reverse and Add! trajectory (presumably) contains exactly n base-4 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 A075421, 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 twelve palindromes, i.e., a(n) = -1 for n > 12.

%C Base-4 analog of A077594.

%H <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>

%e a(4) = 3 since the trajectory of 3 contains the four palindromes 3, 15, 975, 64575 (3, 33, 33033, 3330333 in base 4) and at 20966400 joins the trajectory of 318 = A075421(2) and the trajectories of 1 (A035524) and 2 do not contain exactly four palindromes.

%Y Cf. A075299, A035524, A014192, A075420, A075421, A077594.

%K base,sign

%O 0,1

%A _Klaus Brockhaus_, Jan 28 2004