

A066059


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


15



22, 26, 28, 35, 37, 41, 46, 47, 49, 60, 61, 67, 75, 77, 78, 84, 86, 89, 90, 94, 95, 97, 105, 106, 108, 110, 116, 120, 122, 124, 125, 131, 135, 139, 141, 147, 149, 152, 155, 157, 158, 163, 164, 166, 169, 172, 174, 177, 180, 182, 185, 186, 190, 191, 193, 197, 199
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OFFSET

1,1


COMMENTS

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 nth term of the trajectory.  A.H.M. Smeets, Feb 10 2019


LINKS

A.H.M. Smeets, Table of n, a(n) for n = 1..20000
Klaus Brockhaus, On the'Reverse and Add!' algorithm in base 2
Index entries for sequences related to Reverse and Add!


MATHEMATICA

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 *)


PROG

(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).


CROSSREFS

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


KEYWORD

base,nonn


AUTHOR

Klaus Brockhaus, Dec 04 2001


STATUS

approved



