

A192175


Array of primes determined by distance to next prime, by antidiagonals.


5



2, 3, 7, 5, 13, 23, 11, 19, 31, 89, 17, 37, 47, 359, 139, 29, 43, 53, 389, 181, 199, 41, 67, 61, 401, 241, 211, 113, 59, 79, 73, 449, 283, 467, 293, 1831, 71, 97, 83, 479, 337, 509, 317, 1933, 523, 101, 103, 131, 491, 409, 619, 773, 2113, 1069, 887, 107
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OFFSET

1,1


COMMENTS

Row 1: primes p such that p+1 or p+2 is a prime.
Row r>1: primes p such that the least h for which p+2h is prime is r.
Rows 17: A124588, A023200, A031924, A031926, A031928, A031932, A031924.


LINKS

Table of n, a(n) for n=1..56.


EXAMPLE

Northwest corner:
2.....3.....5.....11....17....29....41
7.....13....19....37....43....67....79
23....31....47....53....61....73....83
89....359...389...401...449...479...491
139...181...241...283...337...409...421
For example, 31 is in row 3 because 31+2*3 is a prime, unlike 31+2*1 and 31+2*2. Every prime occurs exactly once. For each row, it not known whether it is finite.


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[Prime[row[#]] &, {10}]] (* A192175 array *)
Flatten[Table[ Prime[row[k][[n  k + 1]]], {n, 1, 11}, {k, 1, n}]] (* A192175 sequence *)
(* by Peter J. C. Moses, Jun 20 2011 *)


CROSSREFS

Cf. A192176, A192177, A192178, A192179.
Sequence in context: A117928 A064011 A050367 * A294205 A059459 A124440
Adjacent sequences: A192172 A192173 A192174 * A192176 A192177 A192178


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Jun 24 2011


STATUS

approved



