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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 Eric Weisstein's World of Mathematics, Goldbach Partition Wikipedia, Goldbach's conjecture 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.)