

A192178


Array by distance to nearest prime, by antidiagonals.


5



1, 2, 5, 3, 7, 26, 4, 9, 34, 23, 6, 11, 50, 37, 118, 8, 13, 56, 47, 122, 53, 10, 15, 64, 67, 144, 89, 120, 12, 17, 76, 79, 186, 119, 300, 409, 14, 19, 86, 83, 204, 121, 324, 479, 532, 16, 21, 92, 93, 206, 157, 530, 531, 896, 293, 18, 25, 94, 97, 216, 173, 534, 533, 898, 631, 11
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OFFSET

1,2


COMMENTS

Row 1: numbers k such that k = 1 or k = 2 or (k  1 or k + 1) is a prime.
Row r > 1: numbers k such that k + r or k  r is a prime but k + q and k  q are not, for q = 1, 2, ..., r  1.
Every positive integer occurs exactly once, so that as a sequence, A192178 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

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


EXAMPLE

Northwest corner:
1....2....3....4....6....8....10
5....7....9....11...13...15...17
26...34...50...56...64...76...86
23...37...47...67...79...83...93
118..122..144..186..204..206..216
...
For example, 34 is in row 3 recause its distance to the nearest prime is 3.


MATHEMATICA

z = 5000; (* z = number of primes used *)
row[1] = (#1[[1]] &) /@ Cases[Array[{#1, PrimeQ[#1  1]  PrimeQ[#1 + 1]  #1 == 1  #1 == 2} &, {z}], {_, True}];
Do[row[x] = Complement[(#1[[1]] &) /@ Cases[Array[{#1, PrimeQ[#1  x]  PrimeQ[#1 + x]} &, {z}], {_, True}], Flatten[Array[row, {x  1}]]], {x, 2, 10}];
TableForm[Array[row, {10}]] (* A192178 array *)
Flatten[Table[row[k][[n  k + 1]], {n, 1, 11}, {k, 1,
n}]] (* A192178 sequence *)
(* by Peter J. C. Moses, Jun 24 2011 *)


CROSSREFS

Cf. A192175, A192176, A192177, A192179.
Sequence in context: A096878 A249162 A134563 * A201914 A331217 A021398
Adjacent sequences: A192175 A192176 A192177 * A192179 A192180 A192181


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Jun 24 2011


STATUS

approved



