A213012 Trajectory of 26 under the Reverse and Add! operation carried out in base 2.

26, 37, 78, 135, 360, 405, 744, 837, 1488, 1581, 3024, 3213, 6048, 6237, 12192, 12573, 24384, 24765, 48960, 49725, 97920, 98685, 196224, 197757, 392448, 393981, 785664, 788733, 1571328, 1574397, 3144192, 3150333

Offset: 0

Author

Ben Branman, Jun 01 2012

Keywords

• nonn
• base

Comments

26 is the second-smallest number (after 22) whose base 2 trajectory does not contain a palindrome.

lim_{n -> infinity} a(n)/a(n-1) = 2 for n mod 2 = 0.

lim_{n -> infinity} a(n)/a(n-1) = 1 for n mod 2 = 1. - Branman

In 2001, Brockhaus proved that if the binary Reverse and Add trajectory of an integer contains an integer of one of four specific given forms, then the trajectory never reaches a palindrome. In the case of 26, that would be 3(2^(2k + 1) - 2^k), with k = 3 corresponding to 360. - Alonso del Arte, Jun 02 2012

Examples

			In binary, 26 is 11010.
a(1) = 37 because 11010 + 01011 = 100101, or 37.
a(2) = 78 because 100101 + 101001 = 1001110, or 78.
		

Links

• Klaus Brockhaus, On the'Reverse and Add!' algorithm in base 2
• Index entries for sequences related to Reverse and Add!

Crossrefs

Cf. A035522, A061561, A066059, A077076, A077077.

Programs

Mathematica

binRA[n_] := If[Reverse[IntegerDigits[n, 2]] == IntegerDigits[n, 2], n, FromDigits[Reverse[IntegerDigits[n, 2]], 2] + n]; NestList[binRA, 26, 100]