login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
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 n-th term of the trajectory. - A.H.M. Smeets, Feb 10 2019
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).
KEYWORD
base,nonn
AUTHOR
Klaus Brockhaus, Dec 04 2001
STATUS
approved