cp's OEIS Frontend

A234316 Irregular triangle T, read by rows, such that row n lists the larger parts of the Goldbach partitions of 2n (in decreasing order).

%I A234316 #28 Feb 16 2025 08:33:21
%S A234316 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,
%T A234316 23,19,17,29,19,31,29,23,17,31,29,23,19,31,19,37,29,23,37,31,29,23,41,
%U A234316 37,31,43,41,29,23,43,41,37,31,29,47,43,37,31,47,41,29,47,43,41,37,31
%N A234316 Irregular triangle T, read by rows, such that row n lists the larger parts of the Goldbach partitions of 2n (in decreasing order).
%C A234316 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.
%C A234316 This is the companion irregular triangle to A184995. See the first formula. - _Wolfdieter Lang_, May 14 2016
%H A234316 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A234316 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A234316 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A234316 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A234316 T(n,i) = 2n - A184995(n,i).
%F A234316 T(n,i) = n + A182138(n,i). - _Ralf Stephan_, Dec 26 2013
%e A234316 The irregular triangle T(n,i) begins:
%e A234316    n | 2*n | i = 1   2   3   4   5   6 ...
%e A234316   ---+-----+------------------------------
%e A234316    2 |   4 |     2
%e A234316    3 |   6 |     3
%e A234316    4 |   8 |     5
%e A234316    5 |  10 |     7   5
%e A234316    6 |  12 |     7
%e A234316    7 |  14 |    11   7
%e A234316    8 |  16 |    13  11
%e A234316    9 |  18 |    13  11
%e A234316   10 |  20 |    17  13
%e A234316   11 |  22 |    19  17  11
%e A234316   12 |  24 |    19  17  13
%e A234316   13 |  26 |    23  19  13
%e A234316   14 |  28 |    23  17
%e A234316   15 |  30 |    23  19  17
%e A234316   16 |  32 |    29  19
%e A234316   17 |  34 |    31  29  23  17
%e A234316   18 |  36 |    31  29  23  19
%e A234316   19 |  38 |    31  19
%e A234316   20 |  40 |    37  29  23
%e A234316   21 |  42 |    37  31  29  23
%e A234316   22 |  44 |    41  37  31
%e A234316   23 |  46 |    43  41  29  23
%e A234316   24 |  48 |    43  41  37  31  29
%e A234316   25 |  50 |    47  43  37  31
%e A234316   26 |  52 |    47  41  29
%e A234316   27 |  54 |    47  43  41  37  31
%e A234316   28 |  56 |    53  43  37
%e A234316   29 |  58 |    53  47  41  29
%e A234316   30 |  60 |    53  47  43  41  37  31
%e A234316  ... Reformatted and extended. - _Wolfdieter Lang_, May 14 2016
%t A234316 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 *)
%o A234316 (PARI) for(n=2, 18, forprime(p=2, n, if(isprime(2*n-p), print1(2*n-p", ")))) \\ _Ralf Stephan_, Dec 26 2013
%Y A234316 Cf. A182138, A184995.
%K A234316 nonn,tabf
%O A234316 2,1
%A A234316 _Wesley Ivan Hurt_, Dec 23 2013