A132422 - OEIS

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).

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

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OFFSET

1,5

COMMENTS

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

LINKS

Table of n, a(n) for n=1..78.

EXAMPLE

Array begins:

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, ...

...

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.

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

CROSSREFS

Cf. A132423.

Sequence in context: A098802 A048804 A158565 * A065133 A343033 A307239

Adjacent sequences: A132419 A132420 A132421 * A132423 A132424 A132425

KEYWORD

nonn,tabl

AUTHOR

Leroy Quet, Aug 20 2007

EXTENSIONS

More terms from Jinyuan Wang, Aug 10 2021

STATUS

approved