A192176 Index array for A192175 (distance up to next prime), by antidiagonals.

1, 2, 4, 3, 6, 9, 5, 8, 11, 24, 7, 12, 15, 72, 34, 10, 14, 16, 77, 42, 46, 13, 19, 18, 79, 53, 47, 30, 17, 22, 21, 87, 61, 91, 62, 282, 20, 25, 23, 92, 68, 97, 66, 295, 99, 26, 27, 32, 94, 80, 114, 137, 319, 180, 154, 28, 29, 36, 124, 82, 121, 146, 331, 205, 259, 189

Offset: 1

Author

Clark Kimberling, Jun 24 2011

Keywords

• nonn
• tabl

Comments

Row 1: numbers k such that p + 1 or p + 2 is a prime,

where p = (k-th prime).

Row r > 1: numbers k such that if p = (k-th prime) then r = (least h for which p + 2 h) is a prime.

Every positive integer occurs exactly once, so that as a sequence, A192176 is a permutation of the positive integers.

Examples

			Northwest corner:
1....2....3....5....7....10....13
4....6....8....12...14...19....22
9....11...15...16...18...21....23
24...72...77...79...87...92....94
34...42...53...61...68...80....82
...
These are the index numbers of the primes displayed in the Example at A192175; e.g., in that display, the top row begins with 2,3,5,11,17,29,41.
		

Crossrefs

Cf. A192175, A192177, A192178, A192179.

Programs

Mathematica

z = 5000; (* z = number of primes used *)
row[1] = (#1[[1]] &) /@ Cases[Array[{#1, PrimeQ[1 + Prime[#1]] || PrimeQ[2 + Prime[#1]]} &, {z}], {, True}]; Do[row[x] = Complement[(#1[[1]] &) /@ Cases[Array[{#1, PrimeQ[2 x + Prime[#1]]} &, {z}], {, True}],Flatten[Array[row, {x - 1}]]], {x, 2, 16}];
TableForm[Array[row, {16}]]   (* A192176 array *)
Flatten[Table[row[k][[n - k + 1]], {n, 1, 11}, {k, 1, n}]]   (* A192176 sequence *)
(* by Peter J. C. Moses, Jun 20 2011 *)