A198584 -id:A198584 - cp's OEIS frontend

A198589 Odd numbers producing 6 odd numbers in the Collatz iteration.

7, 15, 29, 61, 117, 241, 245, 267, 469, 483, 497, 535, 537, 965, 981, 985, 995, 1069, 1073, 1075, 1877, 1933, 1969, 1971, 1989, 2009, 2141, 2147, 2149, 3861, 3925, 3939, 3941, 3981, 4017, 4019, 4043, 4277, 4293, 4297, 4301, 7509, 7733, 7877, 7885, 7957, 8035

Offset: 1

T. D. Noe, Oct 31 2011

nonn

Vincenzo Librandi and T. D. Noe, Table of n, a(n) for n = 1..1000 (terms 1 to 282 from Vincenzo Librandi)

Cf. A198584.

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; t = {}; Do[If[Length[Select[Collatz[n], OddQ]] == 6, AppendTo[t, n]], {n, 1, 10000, 2}]; t

A198590 Odd numbers producing 7 odd numbers in the Collatz iteration.

Original entry on oeis.org

9, 19, 37, 77, 81, 149, 163, 309, 321, 325, 331, 597, 625, 643, 653, 663, 713, 715, 1237, 1251, 1285, 1301, 1313, 1325, 1339, 1425, 1427, 1431, 1433, 2389, 2501, 2573, 2577, 2613, 2625, 2627, 2653, 2679, 2695, 2851, 2853, 2861, 2865, 2867, 4949, 5005, 5141

Offset: 1

T. D. Noe, Oct 31 2011

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..1046

Cf. A198584.

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; t = {}; Do[If[Length[Select[Collatz[n], OddQ]] == 7, AppendTo[t, n]], {n, 1, 10000, 2}]; t
col7Q[n_]:=Length[Select[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&],OddQ]]==7; Select[ Range[1,5201,2],col7Q] (* Harvey P. Dale, Sep 25 2023 *)

A198591 Odd numbers producing 8 odd numbers in the Collatz iteration.

Original entry on oeis.org

25, 49, 51, 99, 101, 197, 205, 217, 397, 405, 433, 435, 441, 475, 789, 821, 833, 857, 867, 869, 875, 883, 951, 953, 955, 1589, 1621, 1649, 1667, 1713, 1715, 1733, 1741, 1751, 1765, 1785, 1901, 1907, 1911, 3157, 3185, 3285, 3299, 3333, 3427, 3429, 3469, 3477

Offset: 1

T. D. Noe, Oct 31 2011

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..1938

Cf. A198584.

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; t = {}; Do[If[Length[Select[Collatz[n], OddQ]] == 8, AppendTo[t, n]], {n, 1, 10000, 2}]; t

A198592 Odd numbers producing 9 odd numbers in the Collatz iteration.

Original entry on oeis.org

33, 65, 67, 131, 133, 261, 269, 273, 289, 525, 529, 533, 547, 555, 571, 577, 579, 583, 633, 635, 1045, 1059, 1077, 1093, 1099, 1111, 1143, 1155, 1157, 1167, 1177, 1267, 1271, 1273, 2101, 2117, 2123, 2133, 2161, 2189, 2199, 2221, 2285, 2309, 2317, 2321, 2333

Offset: 1

T. D. Noe, Oct 31 2011

nonn

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A198584.

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; t = {}; Do[If[Length[Select[Collatz[n], OddQ]] == 9, AppendTo[t, n]], {n, 1, 10000, 2}]; t
col9Q[n_]:=Count[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#!=1&],?(OddQ[#]&)]==9; Select[ Range[1,2501,2],col9Q] (* _Harvey P. Dale, Dec 10 2023 *)

A342815 Numbers of the form (2^(2j + 6k + 5) - 2^(2*j + 1) - 3)/9, with j,k >= 0.

Original entry on oeis.org

3, 13, 53, 213, 227, 853, 909, 3413, 3637, 13653, 14549, 14563, 54613, 58197, 58253, 218453, 232789, 233013, 873813, 931157, 932053, 932067, 3495253, 3724629, 3728213, 3728269, 13981013, 14898517, 14912853, 14913077, 55924053, 59594069, 59651413, 59652309

Offset: 1

Satya Das, Mar 22 2021

Sequence is a subsequence of A198584. When any term is iterated using the Collatz function, the last odd integer in the trajectory before 1 is of the form (4^(3*m + 2) - 1)/3.

Satya Das, Extension of speeded up Collatz map to the real line

Union with A342816 gives A198584.

Take[Sort[Flatten[Table[(2^(2n1+6n2+5) - 2^(2n1+1) - 3)/9, {n1, 0, 20}, {n2, 0, 20}]]], 50]

seq=[]
for n1 in range(20):
    for n2 in range(20):
        n=(2**(2*n1+6*n2+5) - 2**(2*n1+1) - 3)/9
        seq.append(n)
seq.sort()
print(seq[0:50])

A342816 Numbers of the form (2^(2j + 6k + 10) - 2^(2*j + 2) - 3)/9, with j,k >= 0.

Original entry on oeis.org

113, 453, 1813, 7253, 7281, 29013, 29125, 116053, 116501, 464213, 466005, 466033, 1856853, 1864021, 1864133, 7427413, 7456085, 7456533, 29709653, 29824341, 29826133, 29826161, 118838613, 119297365, 119304533, 119304645, 475354453, 477189461, 477218133

Offset: 1

Satya Das, Mar 22 2021

Sequence is a subsequence of A198584. When any term is iterated using the Collatz function, the last odd integer in the trajectory before 1 is of the form (4^(3*m + 4) - 1)/3.

Satya Das, Extension of speeded up Collatz map to the real line

Union with A342815 gives A198584.

Take[Sort[Flatten[Table[(2^(2n1+6n2+10) - 2^(2n1+2) - 3)/9, {n1, 0, 20}, {n2, 0, 20}]]], 50]

seq=[]
for n1 in range(20):
    for n2 in range(20):
        n=(2**(2*n1+6*n2+10) - 2**(2*n1+2) - 3)/9
        seq.append(n)
seq.sort()
print(seq[0:50])

A353957 a(n) = (85*4^n - 1)/3.

Original entry on oeis.org

113, 453, 1813, 7253, 29013, 116053, 464213, 1856853, 7427413, 29709653, 118838613, 475354453, 1901417813, 7605671253, 30422685013, 121690740053, 486762960213, 1947051840853, 7788207363413, 31152829453653, 124611317814613, 498445271258453, 1993781085033813

Offset: 1

Krishna Kumar Arumugam, Sep 03 2022

When any term in the sequence is iterated using the Collatz function, its trajectory's only odd number before reaching 1 will be 85.

Also, each term would have 2n+10 steps as its stopping time (A006577).

			When n=5, a(5) = 29013 and when iterated using the Collatz function will have the following trajectory: 87040,43520,21760,10880,5440,2720,1360,680,340,170,85,256,128,64,32,16,8,4,2,1

Index entries for linear recurrences with constant coefficients, signature (5,-4).

Subsequence of A198584.

Cf. A006577.

(85*4^Range[25] - 1)/3 (* Wesley Ivan Hurt, Nov 10 2023 *)

a(n) = 85*4^n\3 \\ Charles R Greathouse IV, Sep 09 2022

Simpler definition and more terms from Jon E. Schoenfield, Sep 09 2022

cp's OEIS Frontend

A198589 Odd numbers producing 6 odd numbers in the Collatz iteration.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A198590 Odd numbers producing 7 odd numbers in the Collatz iteration.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A198591 Odd numbers producing 8 odd numbers in the Collatz iteration.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A198592 Odd numbers producing 9 odd numbers in the Collatz iteration.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A342815 Numbers of the form (2^(2*j + 6*k + 5) - 2^(2*j + 1) - 3)/9, with j,k >= 0.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

A342816 Numbers of the form (2^(2*j + 6*k + 10) - 2^(2*j + 2) - 3)/9, with j,k >= 0.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

A353957 a(n) = (85*4^n - 1)/3.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A342815 Numbers of the form (2^(2j + 6k + 5) - 2^(2*j + 1) - 3)/9, with j,k >= 0.

A342816 Numbers of the form (2^(2j + 6k + 10) - 2^(2*j + 2) - 3)/9, with j,k >= 0.