A154722 Triangle read by rows in which row n lists: n, in the center of the row and the pairs of noncomposite numbers that are equidistant to n, as shown below in the example.

1, 1, 2, 3, 1, 3, 5, 1, 3, 4, 5, 7, 3, 5, 7, 1, 5, 6, 7, 11, 1, 3, 7, 11, 13, 3, 5, 8, 11, 13, 1, 5, 7, 9, 11, 13, 17, 1, 3, 7, 10, 13, 17, 19, 3, 5, 11, 17, 19, 1, 5, 7, 11, 12, 13, 17, 19, 23, 3, 7, 13, 19, 23, 5, 11, 14, 17, 23, 1, 7, 11, 13, 15

Offset: 1

Author

Omar E. Pol, Jan 14 2009

Keywords

• easy
• nonn
• tabf

Examples

			Triangle begins:
. . . . . . . . . . . . . . .1
. . . . . . . . . . . . . 1, 2, 3
. . . . . . . . . . . .1, .. 3, .. 5
. . . . . . . . . . 1, .. 3, 4, 5, .. 7
. . . . . . . . ... .. 3, .. 5, .. 7, .. .
. . . . . . . 1, .. .. .. 5, 6, 7, .. .. .,11
. . . . . .1, .. 3, .. .. .. 7, .. .. ..11, ..13
. . . . .. .. 3, .. 5, .. .. 8, .. ..11, ..13, .. .
. . .1, .. .. .. 5, .. 7, .. 9, ..11, ..13, .. .. ..17
. 1, .. 3, .. .. .. 7, .. .,10, .. ..13, .. .. ..17, ..19
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000040, A008578, A154720, A154721, A154723, A154724, A154725, A154726, A154727.

Programs

Maple

isnotcomp:=proc(n)return (n=1 or isprime(n)) end:
for n from 1 to 10 do for k from 1 to 2*n-1 do if(k=n or (isnotcomp(k) and isnotcomp(2*n-k)))then print(k):fi:od:od: # Nathaniel Johnston, Apr 18 2011

Mathematica

Select[Flatten@Table[If[k == n  || ! CompositeQ[k] && ! CompositeQ[2 n - k], k, 0], {n, 10}, {k, 2 n - 1}], # > 0 &]  (* Robert Price, Apr 26 2025 *)

Extensions

a(45) - a(73) from Nathaniel Johnston, Apr 18 2011