A075420 Trajectory of n under the Reverse and Add! operation carried out in base 4 (presumably) does not reach a palindrome.

290, 318, 378, 381, 438, 444, 462, 498, 501, 504, 510, 545, 567, 573, 627, 633, 636, 639, 693, 696, 699, 717, 719, 732, 751, 753, 756, 759, 765, 775, 795, 799, 800, 822, 823, 828, 835, 847, 859, 882, 883, 888, 894, 895, 915, 919, 927, 948, 954, 967, 972

Offset: 1

Author

Klaus Brockhaus, Sep 18 2002

Keywords

• base
• nonn

Comments

Base-4 analog of A023108 (base 10) and A066059 (base 2).

Links

• A.H.M. Smeets, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to Reverse and Add!

Crossrefs

Cf. A023108, A066059, A075421, A075299, A075153.

Programs

Mathematica

limit = 10^3; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
Select[Range[1000],
Length@NestWhileList[# + IntegerReverse[#, 4] &, #, # !=
IntegerReverse[#, 4]  &, 1, limit] == limit + 1 &] (* Robert Price, Oct 16 2019 *)

PARI

{stop=1000; for(n=1,980,k=n; c=0; while(c0,d=divrem(a,4); a=d[1]; rev=4*rev+d[2]); if(rev==k,c=stop+1,k=k+rev; c++)); if(c==stop,print1(n,",")))}

Extensions

Offset changed to 1 by A.H.M. Smeets, Feb 10 2019