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 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. 13
 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 (list; graph; refs; listen; history; text; internal format)
 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 A065070 A070800 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

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Last modified August 19 18:51 EDT 2019. Contains 326133 sequences. (Running on oeis4.)