A091680 Smallest number whose base-4 Reverse and Add! trajectory (presumably) contains exactly n base-4 palindromes, or -1 if there is no such number.

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

Base-4 analog of A077594.

Links

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

Index entries for sequences related to Reverse and Add!

Example

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.

Crossrefs

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

Sequence in context: A013761 A013883 A180701 * A129245 A186553 A075420

Adjacent sequences: A091677 A091678 A091679 * A091681 A091682 A091683

Keyword

base,sign

Author

Klaus Brockhaus, Jan 28 2004

Status

approved