The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A323375

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A323375

Let f(p, q) denote the pair (p + q, wt(p) + wt(q)). a(n) gives the number of iterations of f starting at (n, 1) needed to make p/q an integer, or if no integer is ever reached then a(n) = -1. (Here wt is binary weight, A000120.)
(history; published version)

#22 by N. J. A. Sloane at Sat Feb 02 19:59:32 EST 2019

STATUS

editing

approved

#21 by N. J. A. Sloane at Sat Feb 02 19:59:30 EST 2019

NAME

Let f(p, q) = denote the pair (p + q, A000120wt(p) + A000120wt(q)). a(n) gives the number of iterations of f starting at (n, 1) needed to make p/q an integer, or if no integer is ever reached then a(n) = -1. (Here wt is binary weight, A000120.)

STATUS

approved

editing

#20 by N. J. A. Sloane at Tue Jan 15 20:46:06 EST 2019

STATUS

editing

approved

#19 by N. J. A. Sloane at Tue Jan 15 20:45:55 EST 2019

NAME

Let f(p, q) = ((p + q), (, A000120(p) + A000120(q))). a(n) gives the number of iterations, of f starting at (n, 1), iterating f until the needed to make p/q is an integer, or if no integer is ever reached then a(n) = -1.

STATUS

proposed

editing

Discussion

Tue Jan 15

20:46

N. J. A. Sloane: edited

#18 by Ctibor O. Zizka at Mon Jan 14 13:40:36 EST 2019

STATUS

editing

proposed

Discussion

Mon Jan 14

13:41

Ctibor O. Zizka: yes ! adjusted.

#17 by Ctibor O. Zizka at Mon Jan 14 13:40:31 EST 2019

DATA

1, 3, 3, 3, 1, 2, 1, 11, 4, 10, 1, 3, 4, 9, 2, 19, 1, 18, 1, 1, 7, 17, 7, 7, 6, 5, 6, 6, 1, 4, 15, 5, 16, 4, 1, 2, 4, 3, 1, 14, 3, 13, 13, 13, 12, 12, 12, 1, 6, 12, 2, 5, 5, 11, 1, 5, 13, 10, 4, 1, 12, 3, 9, 3, 3, 1, 2, 1, 1, 40, 2, 8, 8, 39, 3, 7, 7, 9, 2, 3, 1, 3, 37, 37, 37, 5, 36, 36, 3, 1, 8

STATUS

proposed

editing

#16 by Ctibor O. Zizka at Mon Jan 14 13:25:28 EST 2019

STATUS

editing

proposed

Discussion

Mon Jan 14

13:29

Michel Marcus: do you agree that a(47) = 1 ?

#15 by Ctibor O. Zizka at Mon Jan 14 13:25:23 EST 2019

EXAMPLE

n=8; (8, 1) -> (9, 2) -> (11, 3) -> (14, 5) -> (19, 5) -> (24, 5) -> (29, 4) -> (33, 5) -> (38, 4) -> (42, 4) -> 46, 4) -> (50, 5) = . 50/5 = 10 , so a(8) = 11 because it needs 11 iterations to reach until p/q is an integer.

STATUS

proposed

editing

#14 by Ctibor O. Zizka at Mon Jan 14 13:12:06 EST 2019

STATUS

editing

proposed

#13 by Ctibor O. Zizka at Mon Jan 14 13:10:39 EST 2019

NAME

For a non-reduced rational number p/q let Let f(p/, q) = ((p + q) / , (A000120(p) + A000120(q))). a(n) gives the number of iterations, starting at (n/, 1, ), iterating f until the p/q is an integer is reached, , or if no integer is ever reached then a(n) = 0-1.

EXAMPLE

n=98; 9/(8, 1 ) -> (9, 2) -> 10/(11, 3 ) -> (14, 5) -> (19, 5) -> (24, 5) -> (29, 4) -> (33, 5) -> (38, 4) -> 13/(42, 4 ) -> 17/46, 4 ) -> 21(50, 5) = 50/3 5 = 7 10 so a(98) = 4 11 because it needs 4 11 iterations to reach an integer.

n=8; 8/1 -> 9/2 -> 11/3 -> 14/5 -> 19/5 -> 24/5 -> 29/4 -> 33/5 -> 38/4 -> 42/4 -> 46/4 -> 50/5 = 10 so a(8) = 11 because it needs 11 iterations to reach an integer.

STATUS

proposed

editing

Discussion

Mon Jan 14

13:11

Ctibor O. Zizka: adjusted to the proposal of Mr. Markus. This was the way I calculated the first terms.