A159888 - OEIS

%I #37 Jan 14 2024 11:54:46

%S 29,39,41,43,45,55,57,59,93,103,105,107,109,119,121,251,285,295,297,

%T 299,301,311,313,315,349,359,361,363,365,375,377,507,541,551,553,555,

%U 557,567,569,571,605,615,617,619,621,631,633,763,797,807,809,811,813,823,825

%N Numbers congruent to {-5,29,39,41,43,45,55,57,59,93,103,105,107,109,119,121} mod 256.

%C When will this first differ from A159887, the trajectory of 29 under repeated application of the map n -> A102370(n)?

%C A bound on the sequences starting to differ is when the appearance of 2^135 - 135 here is followed by 2^135 - 5. This is because A102370(2^135 - 135) = 2^136 - 5. - _Peter Munn_, Jan 12 2024

%H Vincenzo Librandi, <a href="/A159888/b159888.txt">Table of n, a(n) for n = 1..1000</a>

%H David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL8/Sloane/sloane300.html">Sloping binary numbers: a new sequence related to the binary numbers</a>, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).

%H <a href="/index/Se#sequences_which_agree_for_a_long_time">Index entries for sequences which agree for a long time but are different</a>

%t Select[Range[900],MemberQ[{29, 39, 41, 43, 45, 55, 57, 59, 93, 103, 105, 107, 109, 119, 121, 251}, Mod[#, 256]]&] (* _Harvey P. Dale_, Mar 09 2014 *)

%t LinearRecurrence[{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1},{29,39,41,43,45,55,57,59,93,103,105,107,109,119,121,251,285},55] (* _Ray Chandler_, Jul 15 2015 *)

%o (Magma) [n: n in [1..1000] | n mod 256 in [-5,29,39,41, 43,45,55,57,59,93,103,105,107,109,119,121,251]]; // _Vincenzo Librandi_, Mar 11 2014

%Y Cf. A102370, A159887.

%K nonn,easy

%O 1,1

%A _Philippe Deléham_, Apr 25 2009

%E Corrected by _Harvey P. Dale_, Mar 09 2014

%E Edited by _Peter Munn_, Dec 06 2023