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

0,1

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.

Links

Table of n, a(n) for n=0..20.

Index entries for sequences related to Reverse and Add!

Example

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.

Crossrefs

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

Sequence in context: A084232 A145305 A174890 * A306359 A351542 A044870

Adjacent sequences: A077591 A077592 A077593 * A077595 A077596 A077597

Keyword

base,sign

Author

Klaus Brockhaus, Nov 08 2002

Status

approved