

A171637


Triangle read by rows in which row n lists the distinct primes of the distinct decompositions of 2n into unordered sums of two primes.


10



2, 3, 3, 5, 3, 5, 7, 5, 7, 3, 7, 11, 3, 5, 11, 13, 5, 7, 11, 13, 3, 7, 13, 17, 3, 5, 11, 17, 19, 5, 7, 11, 13, 17, 19, 3, 7, 13, 19, 23, 5, 11, 17, 23, 7, 11, 13, 17, 19, 23, 3, 13, 19, 29, 3, 5, 11, 17, 23, 29, 31, 5, 7, 13, 17, 19, 23, 29, 31, 7, 19, 31, 3, 11, 17, 23, 29, 37, 5, 11
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OFFSET

2,1


COMMENTS

Each entry of the nth row is a prime p from the nth row of A002260 such that 2np is also prime. If A002260 is read as the antidiagonals of a square array, this sequence can be read as an irregular square array (see example below). The nth row has length A035026(n). This sequence is the nonzero subsequence of A154725.  Jason Kimberley, Jul 08 2012


LINKS

T. D. Noe, Rows n = 2..250, flattened
Index entries for sequences related to Goldbach conjecture


EXAMPLE

a(2)=2 because for row 2: 2*2=2+2; a(3)=3 because for row 3: 2*3=3+3; a(4)=3 and a(5)=5 because for row 4: 2*4=3+5; a(6)=3, a(7)=5 and a(8)=7 because for row 5: 2*5=3+7=5+5.
The table starts:
2;
3;
3,5;
3,5,7;
5,7;
3,7,11;
3,5,11,13;
5,7,11,13;
3,7,13,17;
3,5,11,17,19;
5,7,11,13,17,19;
3,7,13,19,23;
5,11,17,23;
7,11,13,17,19,23;
3,13,19,29;
3,5,11,17,23,29,31;
As an irregular square array [Jason Kimberley, Jul 08 2012]:
3 . 3 . 3 . . . 3 . 3 . . . 3 . 3
. . . . . . . . . . . . . . . .
5 . 5 . 5 . . . 5 . 5 . . . 5
. . . . . . . . . . . . . .
7 . 7 . 7 . . . 7 . 7 . .
. . . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . .
11. 11. 11. . . 11
. . . . . . . .
13. 13. 13. .
. . . . . .
. . . . .
. . . .
17. 17
. .
19


MATHEMATICA

Table[ps = Prime[Range[PrimePi[2*n]]]; Select[ps, MemberQ[ps, 2*n  #] &], {n, 2, 50}] (* T. D. Noe, Jan 27 2012 *)


PROG

(Haskell)
a171637 n k = a171637_tabf !! (n2) !! (k1)
a171637_tabf = map a171637_row [2..]
a171637_row n = reverse $ filter ((== 1) . a010051) $
map (2 * n ) $ takeWhile (<= 2 * n) a000040_list
 Reinhard Zumkeller, Mar 03 2014


CROSSREFS

Related triangles: A154720, A154721, A154722, A154723, A154724, A154725, A154726, A154727, A184995.  Jason Kimberley, Sep 03 2011
Cf. A020481 (left edge), A020482 (right edge), A238778 (row sums), A238711 (row products), A000040, A010051.
Sequence in context: A076368 A279931 A071049 * A140187 A214127 A111607
Adjacent sequences: A171634 A171635 A171636 * A171638 A171639 A171640


KEYWORD

nonn,tabf


AUTHOR

JuriStepan Gerasimov, Dec 13 2009


EXTENSIONS

Keyword:tabl replaced by tabf, arbitrarily defined a(1) removed and entries checked by R. J. Mathar, May 22 2010
Definition clarified by N. J. A. Sloane, May 23 2010


STATUS

approved



