A077402 Reverse and Add! carried out in base 3; number of steps needed to reach a palindrome, or -1 if no palindrome is ever reached.

0, 0, 0, 1, 0, 2, 1, 2, 0, 1, 0, 2, 1, 0, 2, 3, 0, 4, 1, 2, 0, 1, 2, 0, 3, 4, 0, 1, 0, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 0, 2, 3, 3, 2, 1, 1, 2, 3, 3, 2, 3, 0, 18, 1, 2, 0, 1, 2, 4, 1, 2, 2, 1, 2, 4, 1, 2, 0, 3, 2, 4, 1, 2, 2, 3, 2, 4, 17, 18, 0, 1, 0, 2, 1, 1, 2, 1, 1, 3, 1, 0, 2, 1, 1, 16, 1, 1, 2, 2, 0, 2, 4, -1, 16, 3, 15, 2, 1, 1, 2, 1, 0, 3, 3, 3, 2, 1, 1, 16, 1

Offset

0,6

Comments

Base-3 analog of A066057 (base 2), A075685 (base 4) and A033665 (base 10). a(103) = -1 is a conjecture (cf. A066450, A077408). For values of n such that presumably a(n) = -1 see A077404.

Links

Table of n, a(n) for n=0..120.

Index entries for sequences related to Reverse and Add!

Example

17 (decimal) = 122 -> 122 + 221 = 1120 -> 1120 + 211 = 2101 -> 2101 + 1012 = 10120 -> 10120 + 2101 = 12221 (palindrome) = 160 (decimal) requires 4 steps, so a(17) = 4.

Prog

(ARIBAS) m := 120; stop := 1000; for n := 0 to m do v := -1; c := 0; k := n; while c < stop do d := k; rev := 0; while d > 0 do rev := 3*rev + (d mod 3); d := d div 3; end; if k = rev then v := c; c := stop; else inc(c); k := k + rev; end; end; write(v, ", "); end;

Crossrefs

Cf. A014190, A066450, A033665, A066057, A075685, A077404, A077405.

Sequence in context: A285677 A036578 A229764 * A287418 A125925 A340795

Adjacent sequences: A077399 A077400 A077401 * A077403 A077404 A077405

Keyword

base,sign

Author

Klaus Brockhaus, Nov 05 2002

Status

approved