A154727 Triangle read by rows in which row n lists all the pairs of prime numbers that are equidistant from n, or only n if there is no such pair, as shown below in the example.

1, 2, 3, 3, 5, 3, 7, 5, 7, 3, 11, 3, 5, 11, 13, 5, 7, 11, 13, 3, 7, 13, 17, 3, 5, 17, 19, 5, 7, 11, 13, 17, 19, 3, 7, 19, 23, 5, 11, 17, 23, 7, 11, 13, 17, 19, 23, 3, 13, 19, 29, 3, 5, 11, 23, 29, 31, 5, 7, 13, 17, 19, 23, 29, 31, 7, 31, 3, 11, 17

Offset

1,2

Comments

If the extended Goldbach conjecture is true, such a pair exists in row n for all n >= 4. - Nathaniel Johnston, Apr 18 2011

Links

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

Wolfram MathWorld, Goldbach Conjecture

Example

Triangle begins:
                          1
                          2
                          3
                       3, .  5
                    3, .  .  .  7
                 .  .  5, .  7, . .
              3, .  .  .  .  .  .  . 11
           3, .  5, .  .  .  .  . 11, . 13
        .  .  5, .  7, .  .  . 11, . 13, .  .
     3, .  .  .  7, .  .  .  .  . 13, .  .  . 17

Maple

print(1):print(2):print(3):for n from 1 to 15 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):fi:od:od: # Nathaniel Johnston, Apr 18 2011

Mathematica

Table[n + Union@ Join[#, -#] /. {} -> {n} &@ Select[DeleteCases[n - Prime@ Range[2, PrimePi@ n], 0], AllTrue[n + # {-1, 1}, PrimeQ] &], {n, 20}] // Flatten (* Michael De Vlieger, Feb 03 2019 *)

Crossrefs

Cf. A000040, A154720, A154721, A154722, A154723, A154724, A154725, A154726.

Sequence in context: A215405 A064921 A064917 * A323075 A367133 A065070

Adjacent sequences: A154724 A154725 A154726 * A154728 A154729 A154730

Keyword

easy,nonn,tabf

Author

Omar E. Pol, Jan 14 2009, Jan 16 2009

Extensions

a(24)-a(70) from Nathaniel Johnston, Apr 18 2011

Status

approved