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Search: id:A054431
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| A054431 |
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Array read by antidiagonals: T(x, y) tells whether (x, y) are coprime (1) or not (0), where (x, y) = (1, 1), (1, 2), (2, 1), (1, 3), (2, 2), (3, 1), ... |
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+0
11
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| 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1
(list; table; graph; listen)
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OFFSET
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1,1
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FORMULA
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a(n) = reduced_residue_set_0_1_array(n)
T(n, k)=T(n, k-n)+T(n-k, k) starting with T(n, k)=0 if n or k are nonpositive and T(1, 1)=1. T(n, k)=A054521(n, k) if n>=k, =A054521(k, n) if n<=k. Anti-diagonal sums are phi(n)=A000010(n). - Henry Bottomley (se16(AT)btinternet.com), May 14 2002
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EXAMPLE
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Rows start: 1,1,1,1,1,1,...; 1,0,1,0,1,0,...; 1,1,0,1,1,0,...; 1,0,1,0,1,0,...; 1,1,1,1,0,1,...; 1,0,0,0,1,0,...; etc.
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MAPLE
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reduced_residue_set_0_1_array := n -> one_or_zero(igcd(((n-((trinv(n)*(trinv(n)-1))/2))+1), ((((trinv(n)-1)*(((1/2)*trinv(n))+1))-n)+1) ));
one_or_zero := n -> `if`((1 = n), (1), (0)); # trinv given at A054425
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CROSSREFS
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Equal to A003989 with non-one values replaced with zeros. Cf. A047999, A054432, A055088.
Sequence in context: A077009 A078556 A047999 this_sequence A106470 A106465 A099990
Adjacent sequences: A054428 A054429 A054430 this_sequence A054432 A054433 A054434
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KEYWORD
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nonn,tabl
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AUTHOR
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Antti Karttunen
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