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

1,2

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.

Links

Table of n, a(n) for n=1..66.

Example

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.

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 *)

Crossrefs

Cf. A192175, A192177, A192178, A192179.

Sequence in context: A256661 A370923 A179216 * A365230 A191711 A163280

Adjacent sequences: A192173 A192174 A192175 * A192177 A192178 A192179

Keyword

nonn,tabl

Author

Clark Kimberling, Jun 24 2011

Status

approved