A077594 Smallest number whose Reverse and Add! trajectory (presumably) contains exactly n palindromes, or -1 if there is no such number.

196, 89, 49, 18, 9, 14, 7, 6, 3, 4, 2, 1, 10000, -1, -1, -1, -1, -1, -1, -1, -1

Offset: 0

Author

Klaus Brockhaus, Nov 08 2002

Keywords

• base
• sign

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 A063048, 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.

Examples

			a(9) = 4 since the trajectory of 4 contains the nine palindromes 4, 8, 77, 1111, 2222, 4444, 8888, 661166, 3654563 and at 7309126 joins the trajectory of 10577 = A063048(6) and no m < 4 contains exactly nine palindromes.
		

Links

• Index entries for sequences related to Reverse and Add!

Crossrefs

Cf. A002113, A006960, A023108, A063048, A063433, A065001, A070742.