A125755 -id:A125755 - cp's OEIS frontend

A125754 Numbers n whose reverse binary representation has the following property: let a 0 mean "halving" and a 1 mean "k -> 3k+1". The number describes an operation k -> f_n(k). If the equation f_n(k) = k has an integer solution, n is a term in the sequence.

2, 4, 10, 17, 18, 20, 24, 36, 42, 140, 145, 170, 200, 292, 561, 594, 660, 682, 792, 1059, 1136, 1553, 1800, 2340, 2730, 4150, 4274, 4297, 4308, 4389, 4433, 4490, 4634, 4696, 4705, 4741, 4804, 4876, 5133, 5164, 5218, 5254, 5400, 5409, 5668

Offset: 1

David Applegate, Feb 02 2007

nonn

Suggested by A125626.

Note that f_n(x) is always a linear function of x.

David Applegate, Table of n, a(n) for n = 1..101

Cf. A125626, A125755, A125756, A125757, A125710, A125711.

A125756 Numbers n whose reverse binary representation has the following property: let a 0 mean "halving" and a 1 mean "k -> 3k+1". The number describes an operation k -> f_n(k). If the equation f_n(k) = k has a positive integer solution, n is a term in the sequence.

Original entry on oeis.org

4, 36, 140, 145, 200, 292, 1059, 1136, 1553, 1800, 2340, 4150, 4274, 4297, 4308, 4389, 4433, 4490, 4634, 4696, 4705, 4741, 4804, 4876, 5133, 5164, 5218, 5254, 5400, 5409, 5668, 5712, 5761, 6244, 6290, 6312, 6448, 6466, 6662, 6800, 6976

Offset: 1

David Applegate, Feb 02 2007

nonn

Suggested by A125626.

Note that f_n(x) is always a linear function of x.

David Applegate, Table of n, a(n) for n = 1..60

Cf. A125626, A125755, A125754, A125757, A125710, A125711.

A125758 Numbers congruent to 4 or 7 (mod 9).

Original entry on oeis.org

4, 7, 13, 16, 22, 25, 31, 34, 40, 43, 49, 52, 58, 61, 67, 70, 76, 79, 85, 88, 94, 97, 103, 106, 112, 115, 121, 124, 130, 133, 139, 142, 148, 151, 157, 160, 166, 169, 175, 178, 184, 187, 193, 196, 202, 205, 211, 214, 220, 223, 229, 232, 238, 241, 247, 250, 256, 259, 265, 268

Offset: 1

N. J. A. Sloane and David Applegate, Feb 02 2007

For a given integer m, write its binary representation in reverse order, as in A125626, A125754, etc.; let a 0 mean "halving" and a 1 mean "k -> 3k+1". Then m specifies an operation on real numbers given by k -> f_m(k). Suppose the equation f_m(k) = k has a positive integer solution for some m. Then we conjecture that the values of k are precisely the terms of this sequence.
25 is a term because we have 25 -> 76 -> 38 -> 19 -> 58 -> 29 -> 88 -> 44 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 25.
In other words, we conjecture that this sequence coincides with A125757 sorted and with duplicates removed.

David Lovler, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A125626, A125754, A125755, A125756, A125757, A125710, A125711.

Select[Range[300],MemberQ[{4,7},Mod[#,9]]&]  (* Harvey P. Dale, Mar 12 2011 *)

From R. J. Mathar, Apr 03 2009: (Start)
a(n) = a(n-1) + a(n-2) - a(n-3) = a(n-2) + 9.
a(n) + a(n+1) = A017185(n).
G.f.: x*(4+3*x+2*x^2)/((1+x)*(x-1)^2). (End)
E.g.f.: 2 + ((9*x - 5/2)*exp(x) - (3/2)*exp(-x))/2. - David Lovler, Aug 21 2022

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A125754 Numbers n whose reverse binary representation has the following property: let a 0 mean "halving" and a 1 mean "k -> 3k+1". The number describes an operation k -> f_n(k). If the equation f_n(k) = k has an integer solution, n is a term in the sequence.

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A125756 Numbers n whose reverse binary representation has the following property: let a 0 mean "halving" and a 1 mean "k -> 3k+1". The number describes an operation k -> f_n(k). If the equation f_n(k) = k has a positive integer solution, n is a term in the sequence.

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A125758 Numbers congruent to 4 or 7 (mod 9).

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