A026098 Triangular array T read by rows: T(1,1)=1, T(2,1)=3, T(2,2)=2; for n >= 3, T(n,1)=prime(n) and for k=2,3,...,n, T(n,k) = m*prime(n+1-k), where m is the least positive integer such that m*p(n+1-k) is not any T(i,j) for 1<=i<=n-1 nor any T(n,j) for j<=k-1.

1, 3, 2, 5, 6, 4, 7, 10, 9, 8, 11, 14, 15, 12, 16, 13, 22, 21, 20, 18, 24, 17, 26, 33, 28, 25, 27, 30, 19, 34, 39, 44, 35, 40, 36, 32, 23, 38, 51, 52, 55, 42, 45, 48, 46, 29, 69, 57, 68, 65, 66, 49, 50, 54, 56, 31, 58, 92, 76, 85, 78, 77, 63, 60, 72, 62, 37, 93, 87, 115, 95, 102, 91, 88, 70, 75, 81, 64

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• tabl

Comments

A permutation of the natural numbers.

Examples

			1;
3, 2;
5, 6, 4;
7, 10, 9, 8;
11, 14, 15, 12, 16;
13, 22, 21, 20, 18, 24;
17, 26, 33, 28, 25, 27, 30;
19, 34, 39, 44, 35,..
		

Links

• Michel Marcus, Rows n=1..100 of triangle, flattened
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse permutation: A070264.

Programs

Mathematica

T[1, 1] = 1; T[2, 1] = 3; T[2, 2] = 2;
T[n_, 1] := Prime[n];
T[n_, k_] := T[n, k] = Module[{m, mp, jtt}, For[m = 1, True, m++, mp = m Prime[n + 1 - k]; jtt = Join[Table[T[i, j], {i, 1, n - 1}, {j, 1, i}] // Flatten, Table[T[n, j], {j, 1, k - 1}]]; If[FreeQ[jtt, mp], Return[mp]]]];
Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 05 2019 *)

PARI

getrow(n, all) = {if (n==1, return ([1])); if (n==2, return ([3, 2])); my(row = vector(n)); row[1] = prime(n); for (k=2, n, my(ok = 0, m = 1, val); until(ok, val = m*prime(n+1-k); if (!setsearch(all, val) && !setsearch(Set(row), val), ok = 1); m++;); row[k] = val;); return (row);}
tabl(nn) = {my(all = []); for (n=1, nn, my(row = getrow(n, all)); print(row); /* for (k=1, n, print1(row[k], ", ")); */ all = Set(concat(all, row)););} \\ Michel Marcus, Sep 04 2019

Extensions

Corrected by David Wasserman, Aug 12 2002

More terms from Michel Marcus, Sep 04 2019