A132422 - OEIS

%I #16 Aug 21 2021 15:52:18

%S 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,

%T 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,

%U 10,1,1,3,5,7,5,17,8,17,9,23,11,1

%N 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).

%C 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.

%e Array begins:

%e   1,  1,  1,  1,  1,  1, ...

%e   1,  2,  3,  2,  3,  2, ...

%e   1,  3,  4,  5,  3,  4, ...

%e   1,  4,  7,  4,  7,  4, ...

%e   1,  5,  6, 13,  5,  6, ...

%e   1,  6, 17,  6, 17,  6, ...

%e   ...

%e 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.

%o (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

%Y Cf. A132423.

%K nonn,tabl

%O 1,5

%A _Leroy Quet_, Aug 20 2007

%E More terms from _Jinyuan Wang_, Aug 10 2021