The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A132422 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A132422

Array read by antidiagonals: A(m,1) = 1 for all positive integers m. A(m,n) = the m-th integer from among those positive integers which are coprime to A(m,n-1).
(history; published version)

#16 by N. J. A. Sloane at Sat Aug 21 15:52:18 EDT 2021

STATUS

proposed

approved

#15 by Jon E. Schoenfield at Tue Aug 10 22:53:27 EDT 2021

STATUS

editing

proposed

#14 by Jon E. Schoenfield at Tue Aug 10 22:53:18 EDT 2021

EXAMPLE

1, 1, 1, 1, 1, 1, ...

1, 2, 3, 2, 3, 2, ...

1, 3, 4, 5, 3, 4, ...

1, 4, 7, 4, 7, 4, ...

1, 5, 6, 13, 5, 6, ...

1, 6, 17, 6, 17, 6, ...

...

STATUS

proposed

editing

#13 by Jinyuan Wang at Tue Aug 10 22:46:21 EDT 2021

STATUS

editing

proposed

#12 by Jinyuan Wang at Tue Aug 10 22:45:40 EDT 2021

DATA

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 2, 4, 4, 1, 1, 3, 5, 7, 5, 1, 1, 2, 3, 4, 6, 6, 1, 1, 3, 4, 7, 13, 17, 7, 1, 1, 2, 5, 4, 5, 6, 8, 8, 1, 1, 3, 3, 7, 6, 17, 13, 15, 9, 1, 1, 2, 4, 4, 13, 6, 7, 14, 13, 10, 1, 1, 3, 5, 7, 5, 17, 8, 17, 9, 23, 11, 1

EXAMPLE

a(m,n):

Array begins:

a(m,1): , 1, 1, 1, 1, 1, ...

a(m,2): 1, 2, 3, 2, 3, 4, 5, 2, ...

a(m,3): 1, 3, 4, 5, 3, 4, 7, 6, ...

1, 4, 7, 4, 7, 4, ...

a(m,4): 1, 2, 5, 4, 6, 13, 5, 6, ...

a(m,5): 1, 3, 3, 7, 5, ...

1, 6, 17, 6, 17, 6, ...

...

PROG

(PARI) A(m, n) = if(n==1, 1, my(k, t=A(m, n-1)); for(c=1, m, until(gcd(k, t)==1, k++)); k); \\ Jinyuan Wang, Aug 10 2021

EXTENSIONS

More terms from Jinyuan Wang, Aug 10 2021

STATUS

proposed

editing

#11 by Jinyuan Wang at Tue Aug 10 08:59:10 EDT 2021

STATUS

editing

proposed

Discussion

Tue Aug 10

15:07

Michel Marcus: T rather than a or A ?  needs keyword more

22:40

Jinyuan Wang: many sequences use A for array and T for triangular

#10 by Jinyuan Wang at Tue Aug 10 08:56:00 EDT 2021

NAME

Array read by antidiagonals: aA(m,1) = 1 for all positive integers m. aA(m,n) = the m-th integer from among those positive integers which are coprime to aA(m,n-1).

COMMENTS

Many, if not all, sequences {aA(m,n)}, for fixed m, are periodic after some point. aA(m,n) = aA(m,n+A132423(n)) for all n > some integer.

EXAMPLE

For example, the positive integers which are coprime to aA(4,2)=4 are 1, 3, 5, 7, 9, ... The 4th of these integers is 7. So aA(4,3) = 7.

KEYWORD

more,nonn,tabl

STATUS

approved

editing

Discussion

Tue Aug 10

08:59

Jinyuan Wang: array in example should do diagonal symmetric transformation (note that A(4,2) = 4) ? I'll add more terms later

#9 by Wesley Ivan Hurt at Wed Dec 07 22:51:40 EST 2016

STATUS

proposed

approved

#8 by Jon E. Schoenfield at Wed Dec 07 22:48:55 EST 2016

STATUS

editing

proposed

#7 by Jon E. Schoenfield at Wed Dec 07 22:48:51 EST 2016

NAME

Array read by anti-diagonalsantidiagonals: a(m,1) = 1, for all positive integers m. a(m,n) = the m-th integer from among those positive integers which are coprime to a(m,n-1).

EXAMPLE

a(m,1): 1, 1, 1, 1, 1, ...

a(m,2): 1, 2, 3, 4, 5, ...

a(m,3): 1, 3, 4, 7, 6, ...

a(m,4): 1, 2, 5, 4, 13, ...

a(m,5): 1, 3, 3, 7, 5, ...

For example, the positive integers which are coprime to a(4,2)=4 are 1, 3, 5, 7, 9, ... The 4th of these integers is 7. So a(4,3) = 7.

STATUS

approved

editing