OFFSET
1,2
COMMENTS
Row 1: numbers k such that k = 1 or k = 2 or k - 1 is a prime.
Row r > 1: numbers k such that k - r is a prime and k - q is not, for q = 1, 2, ..., r - 1.
Every positive integer occurs exactly once, so that as a sequence, A192177 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.
EXAMPLE
Northwest corner:
1....2....3....4....6....8
5....7....9....13...15...19
10...16...22...26...34...40
11...17...23...27...35...41
28...36...52...58...66...78
...
For example, 16 is in row 3 because 16 - 3 is prime, unlike 16 - 1 and 16 - 2.
MATHEMATICA
z = 5000; (* z = number of primes used *)
row[1] = (#1[[1]] &) /@ Cases[Array[{#1, PrimeQ[#1 - 1] || #1 == 1 || #1 == 2} &, {z}], {_, True}];
Do[row[x] = Complement[(#1[[1]] &) /@ Cases[Array[{#1, PrimeQ[#1 - x]} &, {z}], {_, True}], Flatten[Array[row, {x - 1}]]], {x, 2, 10}];
TableForm[Array[row, {10}]] (* A192177 array *)
Flatten[Table[row[k][[n - k + 1]], {n, 1, 11}, {k, 1,
n}]] (* A192177 sequence *)
(* by Peter J. C. Moses, Jun 24 2011 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jun 24 2011
STATUS
approved