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%I #36 Sep 08 2022 08:45:55
%S 2,3,3,3,5,5,3,7,3,5,5,7,3,7,3,5,11,5,7,11,3,7,13,5,11,7,11,13,3,13,3,
%T 5,11,17,5,7,13,17,7,19,3,11,17,5,11,13,19,3,7,13,3,5,17,23,5,7,11,17,
%U 19,3,7,13,19,5,11,23,7,11,13,17,23,3,13,19,5,11,17,29,7,13,17,19,23,29
%N Irregular triangle T, read by rows, in which row n lists the primes p <= n such that 2n-p is also prime.
%C Row n has first entry A020481(n), length A045917(n), and last entry A112823(n).
%C Each row is the prefix to the middle of the corresponding row of A171637.
%C The Goldbach conjecture states that this irregular Goldbach triangle has in each row at least one entry (A045917(n) >= 1). - _Wolfdieter Lang_, May 14 2016
%H Jason Kimberley, <a href="/A184995/b184995.txt">Table of n, a(n) for n = 2..1000 (flattened 2..26552)</a>
%H OEIS (Plot 2), <a href="/plot2a?name1=A198292&name2=A184995&tform1=untransformed&tform2=untransformed&shift=0&radiop1=xy&drawpoints=true">Plot of (n,p)</a>
%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%F T(n,i) = n - A182138(n,i). - _Jason Kimberley_, Sep 25 2012
%e The irregular triangle T(n, i) starts:
%e n, 2*n\i 1 2 3 4 5 6 ...
%e 2, 4 2
%e 3, 6 3
%e 4, 8 3
%e 5, 10 3 5
%e 6, 12 5
%e 7, 14 3 7
%e 8, 16 3 5
%e 9, 18 5 7
%e 10, 20 3 7
%e 11, 22 3 5 11
%e 12, 24 5 7 11
%e 13, 26 3 7 13
%e 14, 28 5 11
%e 15, 30 7 11 13
%e 16, 32 3 13
%e 17, 34 3 5 11 17
%e 18, 36 5 7 13 17
%e 19, 38 7 19
%e 20, 40 3 11 17
%e 21, 42 5 11 13 19
%e 22, 44 3 7 13
%e 23, 46 3 5 17 23
%e 24, 48 5 7 11 17 19
%e 25, 50 3 7 13 19
%e 26, 52 5 11 23
%e 27, 54 7 11 13 17 23
%e 28, 56 3 13 19
%e 29, 58 5 11 17 29
%e 30, 60 7 13 17 19 23 29
%e ... reformatted - _Wolfdieter Lang_, May 14 2016
%t Table[Select[Prime@ Range@ PrimePi@ n, PrimeQ[2 n - #] &], {n, 2, 30}] // Flatten (* _Michael De Vlieger_, May 14 2016 *)
%o (Magma) A184995 := func<n|[p:p in PrimesUpTo(n)|IsPrime(2*n-p)]>;
%o &cat[A184995(n):n in [2..30]];
%Y Related triangles: A154720, A154721, A154722, A154723, A154724, A154725, A154726, A154727, A171637, A182138.
%K nonn,tabf,easy
%O 2,1
%A _Jason Kimberley_, Sep 03 2011
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