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

1,12

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

Links

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

Example

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, ...

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

Crossrefs

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

Sequence in context: A261239 A261214 A143073 * A010816 A133089 A198954

Adjacent sequences: A154722 A154723 A154724 * A154726 A154727 A154728

Keyword

easy,nonn,tabf

Author

Omar E. Pol, Jan 14 2009

Status

approved