A061561 -id:A061561 - cp's OEIS frontend

A092211 a(n) = smallest k such that the base-2 Reverse and Add! trajectory of A075252(n) joins the trajectory of k.

1, 64, 442, 454, 107, 1066, 1081, 1082, 1085, 1115, 1562, 911, 1070, 266, 3355, 98, 3871, 4099, 4152, 1274, 74, 4202, 4262, 4182, 275, 4633, 4666, 4114, 6166, 6374, 9241, 9466, 8312, 16418, 16490, 16601, 16613, 16616, 298, 16748, 16994, 17002

Offset: 1

Klaus Brockhaus, Feb 25 2004

a(n) <= A075252(n); a(n) = A075252(n) iff the trajectory of A075252(n) does not join the trajectory of any smaller number, i.e., A075252(n) is also a term of A092210.
a(n) determines a 1-1-mapping from the terms of A075252 to the terms of A092210. For the inverse mapping cf. A092212.
Base-2 analog of A089493 (base 10) and A091676 (base 4).

			A075252(1) = 22, the trajectory of 22 (A061561) joins the trajectory of 1 = A092210(1) at 48960, so a(1) = 1. A075252(12) = 1575, the trajectory of 1575 joins the trajectory of 911 = A092210(17) at 184680, so a(12) = 911.

Index entries for sequences related to Reverse and Add!

Cf. A075252, A092210, A092212, A061561, A089493, A091676.

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

Original entry on oeis.org

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

Ben Branman, Jun 01 2012

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

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

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

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

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

cp's OEIS Frontend

A092211 a(n) = smallest k such that the base-2 Reverse and Add! trajectory of A075252(n) joins the trajectory of k.

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