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A192177
Array determined by distance down to nearest prime.
5
1, 2, 5, 3, 7, 10, 4, 9, 16, 11, 6, 13, 22, 17, 28, 8, 15, 26, 23, 36, 29, 12, 19, 34, 27, 52, 37, 96, 14, 21, 40, 35, 58, 53, 120, 97, 18, 25, 46, 41, 66, 59, 146, 121, 122, 20, 31, 50, 47, 78, 67, 188, 147, 148, 123, 24, 33, 56, 51, 88, 79, 206, 189, 190, 149, 11
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