

A174349


Array: row n gives the first n numbers i for which the next prime after prime(i) is prime(i)+2n.


2



2, 3, 4, 5, 6, 9, 7, 8, 11, 24, 10, 12, 15, 72, 34, 13, 14, 16, 77, 42, 46, 17, 19, 18, 79, 53, 47, 30, 20, 22, 21, 87, 61, 91, 62, 282, 26, 25, 23, 92, 68, 97, 66, 295, 99, 28, 27, 32, 94, 80, 114, 137, 319, 180, 154, 33, 29, 36, 124, 82, 121, 146, 331, 205, 259, 189
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OFFSET

1,1


COMMENTS

Row 1: A029707
Row 2: A029709
Column 1: A038664.
It is conjectured that every positive integer except 1 occurs in the array.


LINKS

T. D. Noe, Rows n = 1..50 of triangle, flattened
Fred B. Holt and Helgi Rudd, On Polignac's Conjecture, arxiv:1402.1970 [math.NT], 2014.


FORMULA

a(n) = A000720(A174350(n)).  Michel Marcus, Mar 30 2016


EXAMPLE

Corner of the array:
2.....3.....5.....7.....10.....13.....
4.....6.....8.....12....14.....17....
9.....11....15....16....18.....21....
24....72....77....79....87.....92....
34....42....53....61....68.....80....
46....47....91....97....114....121...
Row 1: p(2)=3, p(3)=5, p(5)=11, p(7)=17,... these being the primes for which the next prime is 2 greater.
Row 2: p(4)=7, p(6)=13, p(8)=19,... these being the primes for which the next prime is 4 greater.


MATHEMATICA

rows = 10; t2 = {}; Do[t = {}; p = Prime[2]; While[Length[t] < rows  off + 1, nextP = NextPrime[p]; If[nextP  p == 2*off, AppendTo[t, p]]; p = nextP]; AppendTo[t2, t], {off, rows}]; t3 = Table[t2[[b, a  b + 1]], {a, rows}, {b, a}]; PrimePi /@ t3 (* T. D. Noe, Feb 11 2014 *)


CROSSREFS

Cf. A000040, A000720, A001223, A174350.
Sequence in context: A275583 A257815 A141655 * A099004 A270194 A055170
Adjacent sequences: A174346 A174347 A174348 * A174350 A174351 A174352


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Mar 16 2010


STATUS

approved



