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

1,2

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

Prog

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

Crossrefs

Sequence in context: A351296 A089168 A103127 * A097856 A071593 A192794

Adjacent sequences: A103189 A103190 A103191 * A103193 A103194 A103195

Keyword

nonn,base

Author

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

Status

approved