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A125704
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Table read by antidiagonals: row n contains the positive integers (in order) which are coprime to the n-th prime.
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3
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1, 1, 3, 1, 2, 5, 1, 2, 4, 7, 1, 2, 3, 5, 9, 1, 2, 3, 4, 7, 11, 1, 2, 3, 4, 6, 8, 13, 1, 2, 3, 4, 5, 7, 10, 15, 1, 2, 3, 4, 5, 6, 8, 11, 17, 1, 2, 3, 4, 5, 6, 8, 9, 13, 19, 1, 2, 3, 4, 5, 6, 7, 9, 11, 14, 21, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 16, 23, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 17, 25, 1, 2, 3, 4, 5
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OFFSET
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1,3
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LINKS
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FORMULA
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T(n,m) = m - 1 + floor((m+prime(n)-2)/(prime(n)-1)) where prime(n) = n-th prime. - Benoit Cloitre, Jul 11 2009
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EXAMPLE
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Beginning of table:
1, 3, 5, 7, 9, 11, 13, ...
1, 2, 4, 5, 7, 8, 10, 11, ...
1, 2, 3, 4, 6, 7, 8, 9, 11, ...
1, 2, 3, 4, 5, 6, 8, 9, 10, ...
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MAPLE
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A125704 := proc(n, m) local p, i, a ; p := ithprime(n) ; a := 1 ; for i from 2 to m do a := a+1 ; while gcd(a, p) <> 1 do a := a+1 ; od ; od ; RETURN(a) ; end : maxdiag := 15 ; for d from 1 to maxdiag do for n from d to 1 by -1 do printf("%d, ", A125704(n, d-n+1)) ; od ; od; # R. J. Mathar, Feb 02 2007
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MATHEMATICA
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Table[Function[n, k - 1 + Floor[(k + Prime[n] - 2)/(Prime[n] - 1)]][m - k + 1], {m, 14}, {k, m}] // Flatten (* Michael De Vlieger, Oct 10 2017, after PARI by Benoit Cloitre *)
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PROG
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(PARI) T(n, m)=m-1+floor((m+prime(n)-2)/(prime(n)-1)) \\ Benoit Cloitre, Jul 11 2009
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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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