A092215 Smallest number whose base-2 Reverse and Add! trajectory (presumably) contains exactly n base-2 palindromes, or -1 if there is no such number.

22, 30, 10, 4, 6, 2, 1, 132, 314, 403, 259, 2048, -1, -1, -1, -1

Offset: 0

Author

Klaus Brockhaus, Feb 25 2004

Keywords

• sign
• base

Comments

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.

Base-2 analog of A077594 (base 10) and A091680 (base 4).

Examples

			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.
		

Links

• Index entries for sequences related to Reverse and Add!

Crossrefs

Cf. A035522, A006995, A075252, A077594, A091680.