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

Author

Klaus Brockhaus, Nov 05 2002

Keywords

• base
• nonn

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.

Examples

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

Links

• Index entries for sequences related to Reverse and Add!
• Klaus Brockhaus, On the 'Reverse and Add!' algorithm in base 2

Crossrefs

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

Programs

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;