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A234316 Irregular triangle T, read by rows, such that row n lists the larger parts of the Goldbach partitions of 2n (in decreasing order). 0
2, 3, 5, 7, 5, 7, 11, 7, 13, 11, 13, 11, 17, 13, 19, 17, 11, 19, 17, 13, 23, 19, 13, 23, 17, 23, 19, 17, 29, 19, 31, 29, 23, 17, 31, 29, 23, 19, 31, 19, 37, 29, 23, 37, 31, 29, 23, 41, 37, 31, 43, 41, 29, 23, 43, 41, 37, 31, 29, 47, 43, 37, 31, 47, 41, 29, 47, 43, 41, 37, 31 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Row n has first entry A060308(n), and length A045917(n). If Goldbach's conjecture is true, then each row of the triangle contains at least 1 entry.

This is the companion irregular triangle to A184995. See the first formula. - Wolfdieter Lang, May 14 2016

LINKS

Table of n, a(n) for n=2..72.

Eric Weisstein's World of Mathematics, Goldbach Partition

Wikipedia, Goldbach's conjecture

Index entries for sequences related to Goldbach conjecture

Index entries for sequences related to partitions

FORMULA

T(n,i) = 2n - A184995(n,i).

T(n,i) = n + A182138(n,i). - Ralf Stephan, Dec 26 2013

EXAMPLE

The irregular triangle T(n,i) begins:

   n | 2*n | i = 1   2   3   4   5   6 ...

  ---+-----+------------------------------

   2 |   4 |     2

   3 |   6 |     3

   4 |   8 |     5

   5 |  10 |     7   5

   6 |  12 |     7

   7 |  14 |    11   7

   8 |  16 |    13  11

   9 |  18 |    13  11

  10 |  20 |    17  13

  11 |  22 |    19  17  11

  12 |  24 |    19  17  13

  13 |  26 |    23  19  13

  14 |  28 |    23  17

  15 |  30 |    23  19  17

  16 |  32 |    29  19

  17 |  34 |    31  29  23  17

  18 |  36 |    31  29  23  19

  19 |  38 |    31  19

  20 |  40 |    37  29  23

  21 |  42 |    37  31  29  23

  22 |  44 |    41  37  31

  23 |  46 |    43  41  29  23

  24 |  48 |    43  41  37  31  29

  25 |  50 |    47  43  37  31

  26 |  52 |    47  41  29

  27 |  54 |    47  43  41  37  31

  28 |  56 |    53  43  37

  29 |  58 |    53  47  41  29

  30 |  60 |    53  47  43  41  37  31

... Reformatted and extended. - Wolfdieter Lang, May 14 2016

MATHEMATICA

Table[First /@ DeleteDuplicates@ Map[Sort[{#, 2 n - #}, Greater] &, Select[2 n - Prime@ Range@ PrimePi[2 n], PrimeQ]], {n, 30}] // Flatten (* Michael De Vlieger, May 15 2016 *)

PROG

(PARI) for(n=2, 18, forprime(p=2, n, if(isprime(2*n-p), print1(2*n-p", ")))) \\ Ralf Stephan, Dec 26 2013

CROSSREFS

Cf. A182138, A184995.

Sequence in context: A246258 A126048 A142349 * A284630 A081622 A064143

Adjacent sequences:  A234313 A234314 A234315 * A234317 A234318 A234319

KEYWORD

nonn,tabf

AUTHOR

Wesley Ivan Hurt, Dec 23 2013

STATUS

approved

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Last modified May 19 11:22 EDT 2019. Contains 323391 sequences. (Running on oeis4.)