1,1

The analog of A023108 in base 2.

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

A.H.M. Smeets, Table of n, a(n) for n = 1..20000

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

limit = 10^4; (* Assumes that there is no palindrome if none is found before "limit" iterations *)

Select[Range[200],

Length@NestWhileList[# + IntegerReverse[#, 2] &, #, # !=

IntegerReverse[#, 2] &, 1, limit] == limit + 1 &] (* Robert Price, Oct 14 2019 *)

(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).

Cf. A062128, A023108, A062130, A033865, A058042, A061561, A066057.

Sequence in context: A260990 A260991 A160078 * A084891 A162422 A063940

Adjacent sequences: A066056 A066057 A066058 * A066060 A066061 A066062

base,nonn

Klaus Brockhaus, Dec 04 2001

approved