A154724 Triangle read by rows in which row n lists 2n-1 terms: n, in the center of the row and the pairs of prime numbers that are equidistant to n, with 0's inserted, as shown below in the example.

1, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 3, 4, 5, 0, 0, 0, 0, 3, 0, 5, 0, 7, 0, 0, 0, 0, 0, 0, 5, 6, 7, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 7, 0, 0, 0, 11, 0, 0, 0, 0, 3, 0, 5, 0, 0, 8, 0, 0, 11, 0, 13, 0, 0, 0, 0, 0, 0, 5, 0, 7, 0, 9, 0, 11, 0, 13, 0, 0, 0, 0

Offset: 1

Author

Omar E. Pol, Jan 14 2009

Keywords

• easy
• nonn
• tabf

Examples

			Triangle begins:
                             1
                          0, 2, 0
                       0, 0, 3, 0, 0
                    0, 0, 3, 4, 5, 0, 0
                 0, 0, 3, 0, 5, 0, 7, 0, 0
              0, 0, 0, 0, 5, 6, 7, 0, 0, 0, 0
           0, 0, 3, 0, 0, 0, 7, 0, 0, 0,11, 0, 0
        0, 0, 3, 0, 5, 0, 0, 8, 0, 0,11, 0,13, 0, 0
     0, 0, 0, 0, 5, 0, 7, 0, 9, 0,11, 0,13, 0, 0, 0, 0
  0, 0, 3, 0, 0, 0, 7, 0, 0,10, 0, 0,13, 0, 0, 0,17, 0, 0
		

Links

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

Crossrefs

Cf. A000040, A154720-A154727.

Programs

Maple

for n from 1 to 10 do for k from 1 to 2*n-1 do if(k=n or (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 *)