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

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