A154725 Triangle read by rows in which row n lists 2n-1 terms: The pairs of prime numbers that are equidistant to n, with 0's inserted, as shown below in the example.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 5, 0, 0, 0, 0, 3, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 5, 0, 7, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 3, 0, 5, 0, 0, 0, 0, 0, 11, 0, 13, 0, 0, 0, 0, 0, 0, 5, 0, 7, 0, 0, 0, 11, 0, 13, 0, 0, 0, 0

Offset: 1

Author

Omar E. Pol, Jan 14 2009

Keywords

• easy
• nonn
• tabf

Comments

Each entry of the n-th row is either 0 or a prime p from the 2n-th row of A002260 such that 2n-p is also prime. - Jason Kimberley, Jul 08 2012

Examples

			Triangle begins:
                             0
                          0, 0, 0
                       0, 0, 0, 0, 0
                    0, 0, 3, 0, 5, 0, 0
                 0, 0, 3, 0, 0, 0, 7, 0, 0
              0, 0, 0, 0, 5, 0, 7, 0, 0, 0, 0
           0, 0, 3, 0, 0, 0, 0, 0, 0, 0,11, 0, 0
        0, 0, 3, 0, 5, 0, 0, 0, 0, 0,11, 0,13, 0, 0
     0, 0, 0, 0, 5, 0, 7, 0, 0, 0,11, 0,13, 0, 0, 0, 0
  0, 0, 3, 0, 0, 0, 7, 0, 0, 0, 0, 0,13, 0, 0, 0,17, 0, 0
From _Jason Kimberley_, Jul 08 2012: (Start)
Square array begins:
   3,    3,    3,    0,    3,    3,    0,    3,    3, ...
      0,    0,    0,    0,    0,    0,    0,    0, ...
   5,    5,    5,    0,    5,    5,    0,    5, ...
      0,    0,    0,    0,    0,    0,    0, ...
   7,    7,    7,    0,    7,    7,    0, ...
      0,    0,    0,    0,    0,    0, ...
   0,    0,    0,    0,    0,    0, ...
      0,    0,    0,    0,    0, ...
  11,   11,   11,    0,   11, ...
      0,    0,    0,    0, ...
  13,   13,   13,    0, ...
      0,    0,    0, ...
   0,    0,    0, ...
      0,    0, ...
  17,   17, ...
      0, ...
  19, ...
(End)
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A154720, A154721, A154722, A154723, A154724, A154726, A154727.

Programs

Maple

for n from 1 to 10 do for k from 1 to 2*n-1 do if(not k=n and (isprime(k) and isprime(2*n-k)))then print(k):else print(0):fi:od:od: # Nathaniel Johnston, Apr 18 2011

Mathematica

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