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A132422
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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).
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1
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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
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1,5
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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