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%I #43 Feb 21 2021 13:47:17
%S 2,3,5,7,19,23,31,47,73,103,139,173,211,233,293,313,331,359,383,389,
%T 523,601,727,751,829,929,997,1039,1093,1163,1321,1427,1583,1789,1861,
%U 1877,1879,2029,2089,2803,3061,3163,3457,3463,3529,3613,3769,3917,4003,4027,4057
%N Smallest prime in Goldbach partition of A025018(n).
%C Increasing subsequence of A020481.
%C For n > 2, a(n) ~ (log(A025018(n)))^e/e, while an upper bound could be written as UB(a(n)) = floor(log(A025018(n)))^e/2 (therefore, for any even v such that 12 <= v <= A025018(67) UB is true). It looks that both approximation and UB are true for any n > 2. Assuming the second equation to be true, UB(10^80) = 718967, UB(10^500) = 104745517, etc. - _Sergey Pavlov_, Jan 17 2021
%H N. J. A. Sloane, <a href="/A025019/b025019.txt">Table of n, a(n) for n=1..67</a> (from the web page of Tomás Oliveira e Silva)
%H Mark A. Herkommer, <a href="http://www.herkommer.org/goldbach/goldbach.htm">Goldbach Conjecture Research</a>
%H Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/goldbach.html">Goldbach conjecture verification</a>
%H Jörg Richstein, <a href="http://dx.doi.org/10.1090/S0025-5718-00-01290-4">Verifying the Goldbach conjecture up to 4 * 10^14</a>, Math. Comp., 70 (2001), 1745-1749.
%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%e 1427 and 1583 are two consecutive terms because A020481(167535419) = 1427 and A020481(209955962) = 1583 and for 167535419 < n < 209955962 A020481(n) <= 1427.
%t p = 1; q = {}; Do[ k = 2; While[ !PrimeQ[k] || !PrimeQ[2n - k], k++ ]; If[k > p, p = k; q = Append[q, p]], {n, 2, 10^8}]; q
%Y Cf. A025018, A020481, A097224, A097226.
%K nonn
%O 1,1
%A _David W. Wilson_, Dec 11 1999
%E Edited and extended by _Robert G. Wilson v_, Dec 13 2002
%E More terms and b-file added by _N. J. A. Sloane_, Nov 28 2007
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