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A066059 Integers such that the 'Reverse and Add!' algorithm in base 2 (cf. A062128) does not lead to a palindrome.

%I A066059 #26 Oct 14 2019 21:09:53
%S A066059 22,26,28,35,37,41,46,47,49,60,61,67,75,77,78,84,86,89,90,94,95,97,
%T A066059 105,106,108,110,116,120,122,124,125,131,135,139,141,147,149,152,155,
%U A066059 157,158,163,164,166,169,172,174,177,180,182,185,186,190,191,193,197,199
%N A066059 Integers such that the 'Reverse and Add!' algorithm in base 2 (cf. A062128) does not lead to a palindrome.
%C A066059 The analog of A023108 in base 2.
%C A066059 It seems that for all these numbers it can be proven that they never reach a palindrome. For this it is sufficient to prove this for all seeds as given in A075252. As observed, for all numbers in A075252, lim_{n -> inf} t(n+1)/t(n) is 1 or 2 (1 for even n, 2 for odd n or reverse); i.e., lim_{n -> inf} t(n+2)/t(n) = 2, t(n) being the n-th term of the trajectory. - _A.H.M. Smeets_, Feb 10 2019
%H A066059 A.H.M. Smeets, <a href="/A066059/b066059.txt">Table of n, a(n) for n = 1..20000</a>
%H A066059 Klaus Brockhaus, <a href="/A058042/a058042.txt">On the'Reverse and Add!' algorithm in base 2</a>
%H A066059 <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>
%t A066059 limit = 10^4; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
%t A066059 Select[Range[200],
%t A066059 Length@NestWhileList[# + IntegerReverse[#, 2] &, #, # !=
%t A066059 IntegerReverse[#, 2]  &, 1, limit] == limit + 1 &] (* _Robert Price_, Oct 14 2019 *)
%o A066059 (ARIBAS): For function b2reverse see A066057; function a066059(mx,stop: integer); var k,c,m,rev: integer; begin for k := 1 to mx do c := 0; m := k; rev := b2reverse(m); while m <> rev and c < stop do inc(c); m := m + rev; rev := b2reverse(m); end; if c >= stop then write(k," "); end; end; end; a066059(210,300).
%Y A066059 Cf. A062128, A023108, A062130, A033865, A058042, A061561, A066057.
%K A066059 base,nonn
%O A066059 1,1
%A A066059 _Klaus Brockhaus_, Dec 04 2001