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A300288
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Irregular triangle read by rows: row n lists the numbers k such that -n <= k <= n and gcd(k, 2*n+1) != 1.
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2
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0, 0, 0, -3, 0, 3, 0, 0, -6, -5, -3, 0, 3, 5, 6, 0, 0, -9, -7, -6, -3, 0, 3, 6, 7, 9, 0, -10, -5, 0, 5, 10, -12, -9, -6, -3, 0, 3, 6, 9, 12, 0, 0, -15, -12, -11, -9, -6, -3, 0, 3, 6, 9, 11, 12, 15, -15, -14, -10, -7, -5, 0, 5, 7, 10, 14, 15, 0, -18, -15, -13, -12, -9, -6, -3, 0, 3, 6, 9, 12, 13, 15, 18, 0
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OFFSET
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1,4
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COMMENTS
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Row n contains 2*n+1 - phi(2*n+1) = A053193(n) terms. Row n has just one term (namely 0) if 2*n+1 is prime.
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LINKS
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FORMULA
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EXAMPLE
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Triangle starts:
[01]: 0,
[02]: 0,
[03]: 0,
[04]: -3, 0, 3,
[05]: 0,
[06]: 0,
[07]: -6, -5, -3, 0, 3, 5, 6,
[08]: 0,
[09]: 0,
[10]: -9, -7, -6, -3, 0, 3, 6, 7, 9,
[11]: 0,
[12]: -10, -5, 0, 5, 10,
[13]: -12, -9, -6, -3, 0, 3, 6, 9, 12,
[14]: 0,
[15]: 0,
[16]: -15, -12, -11, -9, -6, -3, 0, 3, 6, 9, 11, 12, 15,
[17]: -15, -14, -10, -7, -5, 0, 5, 7, 10, 14, 15,
[18]: 0,
[19]: -18, -15, -13, -12, -9, -6, -3, 0, 3, 6, 9, 12, 13, 15, 18,
[20]: 0,
...
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MATHEMATICA
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A300288row[n_]:=With[{q=2n+1}, If[PrimeQ[q], {0}, Select[Range[-n, n], GCD[#, q]!=1&]]]; Array[A300288row, 20] (* Paolo Xausa, Nov 10 2023 *)
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PROG
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(PARI) is(n, k)= ( gcd(k, 2*n+1)!=1 );
for (n=1, 33, for (k=-n, +n, if (is(n, k), print1(k, ", ") ); ); );
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CROSSREFS
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KEYWORD
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sign,tabf
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AUTHOR
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STATUS
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approved
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