A077408 Trajectory of 103 under the Reverse and Add! operation carried out in base 3, written in base 10.

103, 230, 436, 776, 2424, 3856, 7400, 20856, 30928, 60920, 220248, 242704, 432896, 857152, 1460408, 2754688, 5134016, 16206744, 24437488, 44623424, 138104472, 201737128, 401511824, 1438324704, 1601682040, 2820726320, 5622321088

Offset

0,1

Comments

103 = A077405(0) is conjectured (cf. A066450) to be the smallest number such that the Reverse and Add! algorithm in base 3 does not lead to a palindrome. Its trajectory does not exhibit any recognizable regularity, so that the method by which the base-2 trajectories of 22 (cf. A061561), 77 (cf. A075253), 442 (cf. A075268) etc. as well as the base-4 trajectories of 318 (cf. A075153), 266718 (cf. A075466), 270798 (cf. A075467) etc. can be proved to be palindrome-free (cf. Links), is not applicable here.

Links

Table of n, a(n) for n=0..26.

Index entries for sequences related to Reverse and Add!

Klaus Brockhaus, On the 'Reverse and Add!' algorithm in base 2

Example

103 (decimal) = 10211 -> 10211 + 11201 = 22112 = 230 (decimal).

Prog

(ARIBAS) m := 103; stop := 28; c := 0; while c < stop do write(m:group(0), ", "); k := m; rev := 0; while k > 0 do rev := 3*rev + (k mod 3); k := k div 3; end; inc(c); m := m+rev; end;

Crossrefs

Cf. A058042, A077405, A066450, A061561, A075253, A075268, A075153, A075466, A075467.

Sequence in context: A134551 A140006 A142911 * A134214 A200732 A033204

Adjacent sequences: A077405 A077406 A077407 * A077409 A077410 A077411

Keyword

base,nonn

Author

Klaus Brockhaus, Nov 05 2002

Status

approved