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%I #27 Feb 17 2018 10:58:44
%S 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 23,19,17,29,19,31,29,23,17,31,29,23,19,31,19,37,29,23,37,31,29,23,41,
%U 37,31,43,41,29,23,43,41,37,31,29,47,43,37,31,47,41,29,47,43,41,37,31
%N Irregular triangle T, read by rows, such that row n lists the larger parts of the Goldbach partitions of 2n (in decreasing order).
%C 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 This is the companion irregular triangle to A184995. See the first formula. - _Wolfdieter Lang_, May 14 2016
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F T(n,i) = 2n - A184995(n,i).
%F T(n,i) = n + A182138(n,i). - _Ralf Stephan_, Dec 26 2013
%e The irregular triangle T(n,i) begins:
%e n | 2*n | i = 1 2 3 4 5 6 ...
%e ---+-----+------------------------------
%e 2 | 4 | 2
%e 3 | 6 | 3
%e 4 | 8 | 5
%e 5 | 10 | 7 5
%e 6 | 12 | 7
%e 7 | 14 | 11 7
%e 8 | 16 | 13 11
%e 9 | 18 | 13 11
%e 10 | 20 | 17 13
%e 11 | 22 | 19 17 11
%e 12 | 24 | 19 17 13
%e 13 | 26 | 23 19 13
%e 14 | 28 | 23 17
%e 15 | 30 | 23 19 17
%e 16 | 32 | 29 19
%e 17 | 34 | 31 29 23 17
%e 18 | 36 | 31 29 23 19
%e 19 | 38 | 31 19
%e 20 | 40 | 37 29 23
%e 21 | 42 | 37 31 29 23
%e 22 | 44 | 41 37 31
%e 23 | 46 | 43 41 29 23
%e 24 | 48 | 43 41 37 31 29
%e 25 | 50 | 47 43 37 31
%e 26 | 52 | 47 41 29
%e 27 | 54 | 47 43 41 37 31
%e 28 | 56 | 53 43 37
%e 29 | 58 | 53 47 41 29
%e 30 | 60 | 53 47 43 41 37 31
%e ... Reformatted and extended. - _Wolfdieter Lang_, May 14 2016
%t 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 (PARI) for(n=2, 18, forprime(p=2, n, if(isprime(2*n-p), print1(2*n-p", ")))) \\ _Ralf Stephan_, Dec 26 2013
%Y Cf. A182138, A184995.
%K nonn,tabf
%O 2,1
%A _Wesley Ivan Hurt_, Dec 23 2013
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