A075299 - OEIS

%I #12 Oct 18 2019 21:13:42

%S 290,835,1610,4195,17060,23845,46490,89080,138125,255775,506510,

%T 1238395,5127260,8616205,15984335,31949470,79793675,315404860,

%U 569392925,1060061935,2114961710,5206421995,20997654620,35262166285

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

%C 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.

%H Klaus Brockhaus, <a href="/A058042/a058042.txt">On the 'Reverse and Add!' algorithm in base 2</a>

%H David J. Seal, <a href="http://www.mathpages.com/home/dseal.htm">Results</a>

%H <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>

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

%t NestWhileList[# + IntegerReverse[#, 4] &, 290,  # !=

%t IntegerReverse[#, 4] &, 1, 23] (* _Robert Price_, Oct 18 2019 *)

%o (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)}

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

%K base,nonn

%O 0,1

%A _Klaus Brockhaus_, Sep 12 2002