A103192 Trajectory of 1 under repeated application of the function n -> A102370(n).

1, 3, 5, 15, 17, 19, 21, 31, 33, 35, 37, 47, 49, 51, 53, 63, 65, 67, 69, 79, 81, 83, 85, 95, 97, 99, 101, 111, 113, 115, 117, 127, 129, 131, 133, 143, 145, 147, 149, 159, 161, 163, 165, 175, 177, 179, 181, 191, 193, 195, 197, 207, 209, 211, 213, 223, 225, 227, 229, 239, 241

Offset: 1

Author

N. J. A. Sloane, David Applegate, Benoit Cloitre and Philippe Deléham, Mar 25 2005

Keywords

• nonn
• base

Comments

Agrees with A103127 for the first 511 terms, but then diverges. If a(n) is the present sequence and b(n) is A103127 we have:

.n...a(n)..b(n)..difference

.....................

509, 2033, 2033, 0

510, 2035, 2035, 0

511, 2037, 2037, 0

512, 4095, 2047, 2048

513, 4097, 2049, 2048

514, 4099, 2051, 2048

515, 4101, 2053, 2048

516, 4111, 2063, 2048

.....................

The sequence may be computed as follows (from Philippe Deléham, May 08 2005).

Start with -1, 1. Then add powers of 2 whose exponent n is not in A034797: 1, 3, 11, 2059, 2^2059 + 2059, ... This gives

Step 0: -1, 1

Step 1: add 2^2 = 4, getting 3, 5 and thus -1, 1, 3, 5.

Step 2: add 2^4 = 16, getting 15, 17, 19, 21 and thus -1, 1, 3, 5, 15, 17, 19, 21

Step 3: add 2^5 = 32, getting 31, 33, 35, 37, 47, 49, 51, 53 and thus -1, 1, 3, 5, 15, 17, 19, 21, 31, 33, 35, 37, 47, 49, 51, 53, etc.

The jump 2037 --> 4095 for n = 510 -> 511 is explained by the fact that we pass directly from 2^10 to 2^12 since 11 belongs to A034797.

The trajectories of 2 (A103747) and 7 (A103621) may surely be obtained in a similar way.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].
• David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.
• Index entries for sequences which agree for a long time but are different

Programs

Haskell

a103192 n = a103192_list !! (n-1)
a103192_list = iterate (fromInteger . a102370) 1
-- Reinhard Zumkeller, Jul 21 2012