A299714 Irregular triangle read by rows: row n contains numbers k such that 1<=k<=2*n+1 and gcd(n-k, 2*n+1) != 1.
1, 2, 3, 1, 4, 7, 5, 6, 1, 2, 4, 7, 10, 12, 13, 8, 9, 1, 3, 4, 7, 10, 13, 16, 17, 19, 11, 2, 7, 12, 17, 22, 1, 4, 7, 10, 13, 16, 19, 22, 25, 14, 15, 1, 4, 5, 7, 10, 13, 16, 19, 22, 25, 27, 28, 31, 2, 3, 7, 10, 12, 17, 22, 24, 27, 31, 32, 18, 1, 4, 6, 7, 10, 13, 16, 19, 22, 25, 28, 31, 32, 34, 37, 20, 21, 1, 2, 4, 7, 10, 12, 13
Offset: 1
Examples
Triangle starts: [01]: [1] [02]: [2] [03]: [3] [04]: [1, 4, 7] [05]: [5] [06]: [6] [07]: [1, 2, 4, 7, 10, 12, 13] [08]: [8] [09]: [9] [10]: [1, 3, 4, 7, 10, 13, 16, 17, 19] [11]: [11] [12]: [2, 7, 12, 17, 22] [13]: [1, 4, 7, 10, 13, 16, 19, 22, 25] [14]: [14] [15]: [15] [16]: [1, 4, 5, 7, 10, 13, 16, 19, 22, 25, 27, 28, 31] [17]: [2, 3, 7, 10, 12, 17, 22, 24, 27, 31, 32] [18]: [18] ...
Links
- Paolo Xausa, Table of n, a(n) for n = 1..11968 (rows 1..250 of the triangle, flattened)
Crossrefs
Cf. A300288.
Programs
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Maple
T:= n-> select(k-> igcd(n-k, 2*n+1)<>1, [$1..2*n+1])[]: seq(T(n), n=1..25); # Alois P. Heinz, Mar 09 2018
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Mathematica
A299714row[n_]:=With[{q=2n+1},If[PrimeQ[q],{n},Select[Range[q],GCD[n-#,q]!=1&]]];Array[A299714row,20] (* Paolo Xausa, Nov 10 2023 *)
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PARI
is(n,k)= ( gcd(n-k, 2*n+1)!=1 ); for (n=1, 33, for (k=1, 2*n+1, if ( is(n,k), print1(k,", ") ); ); );
Formula
T(n,k) = A300288(n,k) - n.
Comments