A277215 -id:A277215 - cp's OEIS frontend

A277874 a(n) is the last number in the (2n+1)-element alternating sequence of x/2 and (3x+1) iterations starting with A277215(n).

0, 40, 16, 52, 160, 9232, 18952, 4372, 13120, 39364, 118096, 2480056, 5314408, 35075104, 9565936, 28697812, 86093440, 1807962280, 8523250756, 2324522932, 6973568800, 20920706404, 62762119216, 188286357652, 564859072960, 11862040532200, 25418658283288, 15251194969972, 45753584909920, 960825283108360

Offset: 0

Hartmut F. W. Hoft, Nov 03 2016

nonn

a(n) has the form 2*(q*3^n - 1) where q is the smallest odd number so that the alternating Collatz sequence of 2n+1 elements starting at 2*(q*2^n - 1) ends at the maximum of its Collatz trajectory.
Subsequence of a(n) when q=1 is a subsequence of A100774.
Conjecture: this sequence is infinite.

			a(0) = 0 = 2*(1*3^0 - 1) since it is the start and end of the first alternating sequence of 1 element and the maximum of its trajectory.
a(5) = 9232 = 2*(19*3^5 - 1) is the last element in the first alternating sequence of 11 elements [1214, 607, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232] that ends in the trajectory maximum.

Cf. A100774, A277215.

(* we use function altdata[] from A277215 *)
a277874[n_]:=Map[#[[4]]&, altdata[2,n]]
Join[{0,40}, a277874[29]] (*sequence data*)

A277875 a(n) is the odd multiplier q in the expressions 2(q2^n - 1) and 2(q3^n - 1) of numbers A277215(n) and A277874(n), respectively.

Original entry on oeis.org

1, 7, 1, 1, 1, 19, 13, 1, 1, 1, 1, 7, 5, 11, 1, 1, 1, 7, 11, 1, 1, 1, 1, 1, 1, 7, 5, 1, 1, 7, 1, 1, 1, 1, 1, 11, 5, 1, 1, 1, 1, 1, 1, 1, 1, 7, 5, 1, 1, 7, 1, 1, 1, 7, 1, 1, 1, 7, 5, 11, 1, 7, 5, 1, 1, 7, 1, 1, 1, 11, 1, 1, 1, 1, 1, 11, 1, 7, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1

Offset: 0

Hartmut F. W. Hoft, Nov 03 2016

nonn

The position numbers for odd numbers 5, 7, 11, 13 and 19 for the first 200 numbers in the sequence are listed in the Comments section of A277215.

			a(0) = 1 since 0 = 2*(1*2^0 - 1) is the start and end of the first alternating sequence of 1 element and the maximum of its trajectory.
a(5) = 19 since 9232 = 2*(19*3^5 - 1) is the last element in the first alternating sequence of 11 elements - 1214, 607, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232 - that ends in the trajectory maximum.

Cf. A277215, A277874.

(* we use function altdata[] from A277215 *)
a277875[n_]:=Map[#[[2]]&, altdata[2,n]]
Join[{1,7}, a277875[99]] (* sequence data *)

cp's OEIS Frontend

A277874 a(n) is the last number in the (2n+1)-element alternating sequence of x/2 and (3x+1) iterations starting with A277215(n).

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A277875 a(n) is the odd multiplier q in the expressions 2(q2^n - 1) and 2(q3^n - 1) of numbers A277215(n) and A277874(n), respectively.

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cp's OEIS Frontend

A277874 a(n) is the last number in the (2n+1)-element alternating sequence of x/2 and (3x+1) iterations starting with A277215(n).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A277875 a(n) is the odd multiplier q in the expressions 2*(q*2^n - 1) and 2*(q*3^n - 1) of numbers A277215(n) and A277874(n), respectively.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A277875 a(n) is the odd multiplier q in the expressions 2(q2^n - 1) and 2(q3^n - 1) of numbers A277215(n) and A277874(n), respectively.