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

0,1

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.

Links

Table of n, a(n) for n=0..23.

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

David J. Seal, Results

Index entries for sequences related to Reverse and Add!

Example

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

Mathematica

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

Prog

(PARI) {m=290; stop=26; c=0; while(c<stop, print1(k=m, ", "); rev=0; while(k>0, d=divrem(k, 4); k=d[1]; rev=4*rev+d[2]); c++; m=m+rev)}

Crossrefs

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

Sequence in context: A090839 A158255 A295483 * A031712 A251049 A108881

Adjacent sequences: A075296 A075297 A075298 * A075300 A075301 A075302

Keyword

base,nonn

Author

Klaus Brockhaus, Sep 12 2002

Status

approved