A075299 Trajectory of 290 under the Reverse and Add! operation carried out in base 4, written in base 10.

290, 835, 1610, 4195, 17060, 23845, 46490, 89080, 138125, 255775, 506510, 1238395, 5127260, 8616205, 15984335, 31949470, 79793675, 315404860, 569392925, 1060061935, 2114961710, 5206421995, 20997654620, 35262166285

Offset: 0

Author

Klaus Brockhaus, Sep 12 2002

Keywords

• base
• nonn

Comments

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

Examples

			290 (decimal) = 10202 -> 10202 + 20201 = 31003 = 835 (decimal).
		

Links

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

Crossrefs

Cf. A066450, A075153, A058042, A061561, A075253, A075268.

Programs

Mathematica

NestWhileList[# + IntegerReverse[#, 4] &, 290,  # !=
IntegerReverse[#, 4] &, 1, 23] (* Robert Price, Oct 18 2019 *)

PARI

{m=290; stop=26; c=0; while(c0,d=divrem(k,4); k=d[1]; rev=4*rev+d[2]); c++; m=m+rev)}