A154723 Triangle read by rows in which row n lists all the pairs of noncomposite numbers that are equidistant from n, or only n if there are no such pairs, as shown below in the example.

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

Offset

1,3

Comments

If the extended Goldbach conjecture is true, such a pair exists in row n for all n >= 2. - Nathaniel Johnston, Apr 18 2011

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..8000

Abel Jansma, E_8 Symmetry Structures in the Ising model, Master's thesis, University of Amsterdam, 2018.

Wolfram MathWorld, Goldbach Conjecture

Example

Triangle begins:
                             1
                          1,    3
                       1,          5
                    1,    3,    5,    7
                       3,          7,
              1,          5,    7,         11
           1,    3,                     11,   13
              3,    5,               11,   13,
     1,          5,    7,         11,   13,         17
  1,    3,          7,               13,         17,   19

Maple

isnotcomp:=proc(n)return (n=1 or isprime(n)) end:
print(1):for n from 1 to 10 do for k from 1 to 2*n-1 do if(not k=n and (isnotcomp(k) and isnotcomp(2*n-k)))then print(k):fi:od:od: # Nathaniel Johnston, Apr 18 2011

Mathematica

Table[If[Length@ # == 1, #, DeleteCases[#, n]] &@ Union@ Flatten@ Select[IntegerPartitions[2 n, {2}], AllTrue[#, ! CompositeQ@ # &] &], {n, 17}] // Flatten (* Michael De Vlieger, Dec 06 2018 *)

Crossrefs

Cf. A000040, A008578, A154720, A154721, A154722, A154724, A154725, A154726, A154727.

Sequence in context: A037227 A056753 A243158 * A273262 A274532 A254765

Adjacent sequences: A154720 A154721 A154722 * A154724 A154725 A154726

Keyword

easy,nonn,tabf

Author

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

Extensions

a(36)-a(70) from Nathaniel Johnston, Apr 18 2011

Status

approved