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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
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
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 *)
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