A192179 Array determined by distance to next prime, by antidiagonals.

1, 2, 3, 4, 5, 8, 6, 9, 14, 7, 10, 11, 20, 13, 24, 12, 15, 26, 19, 32, 23, 16, 17, 34, 25, 48, 31, 90, 18, 21, 38, 33, 54, 47, 120, 89, 22, 27, 44, 37, 62, 53, 142, 119, 118, 28, 29, 50, 43, 74, 61, 184, 141, 140, 117, 30, 35, 56, 49, 84, 73, 204, 183, 182, 139, 116

Offset

1,2

Comments

Row r : numbers k such that r = (least positive integer h for which k + h is a prime).

Every positive integer occurs exactly once, so that as a sequence, A192179 is a permutation of the positive integers.

For r>1, the numbers in row r have the parity of r-1; e.g., the numbers in row 2 are odd.

Links

Ivan Neretin, Table of n, a(n) for n = 1..5050

Example

Northwest corner:
1....2....4....6....10....12
3....5....9....11...15....17
8....14...20...26...34....38
7....13...19...25...33....37
24...32...48...54...62....74
...
For example, 14 is in row 3 because 14 + 3 is a prime, unlike 14 + 1 and 14 + 2.

Mathematica

z = 5000;  (* z = number of primes used *)
Do[row[x] = Complement[(#1[[1]] &) /@ Cases[({#1 - x, PrimeQ[#1]} &) /@ (Range[z] + x), {_, True}],
   Flatten[Array[row, {x - 1}]]], {x, 1, 10}]
TableForm[Array[row, {10}]]    (* A192179 array *)
Flatten[Table[row[k][[n - k + 1]], {n, 1, 11}, {k, 1,
   n}]]   (* A192179 sequence *)
(* Peter J. C. Moses, Jun 24 2011 *)

Crossrefs

Cf. A192175, A192176, A192177, A192178.

Sequence in context: A354125 A339024 A355429 * A118462 A219360 A275877

Adjacent sequences: A192176 A192177 A192178 * A192180 A192181 A192182

Keyword

nonn,tabl

Author

Clark Kimberling, Jun 24 2011

Status

approved