A159887 -id:A159887 - cp's OEIS frontend

A103747 Trajectory of 2 under repeated application of the map n -> A102370(n).

2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, 186, 254, 258, 262, 266, 270, 274, 278, 282, 286, 290, 294, 298, 302, 306, 310, 314, 382, 386, 390, 394, 398, 402, 406, 410, 414, 418, 422

Offset: 1

Benoit Cloitre and David Applegate, Mar 25 2005

Although it initially appears that a(n)-8n is the 16-periodic sequence {-2,-6,-10,-14,-18,-22,-26,-30,-34,-38,-42,-46,-50,-54,6,2}, this pattern eventually breaks down. However, the first divergence occurs beyond the first 400 million terms.

(a(n)) agrees with the 16-periodic sequence up to a(2^67-1) = 2^70 - 70, but then diverges with a(2^67) = 2^71 - 2. - Charlie Neder, Feb 07 2019

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], preprint, 2005.
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

Cf. A102370, A132417.

Trajectories of other numbers: A103192 (1), A103621 (7), A158953 (12), A159887 (29).

a103747 n = a103747_list !! (n-1)
a103747_list = iterate (fromInteger . a102370) 2
-- Reinhard Zumkeller, Jul 21 2012

Edited by Peter Munn, Jan 13 2024

A103621 Trajectory of 7 under repeated application of the map n -> A102370(n).

Original entry on oeis.org

7, 9, 11, 13, 23, 25, 27, 61, 71, 73, 75, 77, 87, 89, 91, 125, 135, 137, 139, 141, 151, 153, 155, 189, 199, 201, 203, 205, 215, 217, 219, 253, 263, 265, 267, 269, 279, 281, 283, 317, 327, 329, 331, 333, 343, 345, 347, 381, 391, 393, 395, 397, 407, 409, 411, 445

Offset: 1

Philippe Deléham, Mar 31 2005

Initially, first differences are 8-periodic: 2,2,2,10,2,2,34,10. [Unsigned comment made accurate by Peter Munn, Jan 13 2024]

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.

Cf. A102370.

Trajectories of other numbers A103192 (1), A103747 (2), A158953 (12), A159887 (29).

f[n_] := Block[{k = 1, s = 0, l = Max[2, Floor[ Log[2, n + 1] + 2]]}, While[k < l, If[ Mod[n + k, 2^k] == 0, s = s + 2^k]; k++ ]; s + n]; NestList[f, 7, 55] (* Robert G. Wilson v, Mar 30 2005 *)

Conjectures from Chai Wah Wu, Feb 01 2018: (Start)
a(n) = a(n-1) + a(n-8) - a(n-9) for n > 9.
G.f.: x*(3*x^8 + 34*x^7 + 2*x^6 + 2*x^5 + 10*x^4 + 2*x^3 + 2*x^2 + 2*x + 7)/(x^9 - x^8 - x + 1). (End)
The above conjectures are incompatible with A102370(2^37-37) = 2^38-3. - Peter Munn, Jan 13 2024

More terms from Robert G. Wilson v, Mar 30 2005

A158953 Trajectory of 12 under repeated application of the map n -> A102370(n).

Original entry on oeis.org

12, 28, 44, 60, 76, 92, 108, 124, 140, 156, 172, 188, 204, 220, 236, 252, 268, 284, 300, 316, 332, 348, 364, 380, 396, 412, 428, 444, 460, 476, 492, 508, 524, 540, 556, 572, 588, 604, 620, 636, 652, 668, 684, 700, 716, 732, 748, 764, 780, 796, 812, 828, 844

Offset: 1

Philippe Deléham, Apr 01 2009

Coincides with A098502 for at least 1400 terms. - R. J. Mathar, Apr 16 2009

Agrees with A098502 for the first 65535 terms. A098502(65535) = a(65535) = 1048556 = 2^20 - 20. A098502(65536) = 1048572 = 2^20 - 4; a(65536) = 2097148 = 2^21 - 4. - Philippe Deléham, Jan 05 2023

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. Preprint versions: [pdf, ps].
Index entries for sequences which agree for a long time but are different

Cf. A098502, A102370.

Trajectories of other numbers: A103192 (1), A103747 (2), A103621 (7), A159887 (29).

A159888 Numbers congruent to {-5,29,39,41,43,45,55,57,59,93,103,105,107,109,119,121} mod 256.

Original entry on oeis.org

29, 39, 41, 43, 45, 55, 57, 59, 93, 103, 105, 107, 109, 119, 121, 251, 285, 295, 297, 299, 301, 311, 313, 315, 349, 359, 361, 363, 365, 375, 377, 507, 541, 551, 553, 555, 557, 567, 569, 571, 605, 615, 617, 619, 621, 631, 633, 763, 797, 807, 809, 811, 813, 823, 825

Offset: 1

Philippe Deléham, Apr 25 2009

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

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

Vincenzo Librandi, 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, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
Index entries for sequences which agree for a long time but are different

Cf. A102370, A159887.

[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

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 *)
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 *)

Corrected by Harvey P. Dale, Mar 09 2014

Edited by Peter Munn, Dec 06 2023

cp's OEIS Frontend

A103747 Trajectory of 2 under repeated application of the map n -> A102370(n).

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A103621 Trajectory of 7 under repeated application of the map n -> A102370(n).

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A158953 Trajectory of 12 under repeated application of the map n -> A102370(n).

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A159888 Numbers congruent to {-5,29,39,41,43,45,55,57,59,93,103,105,107,109,119,121} mod 256.

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