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a(n) = least 2k such that p is the least prime in a Goldbach partition of 2k, where p = prime(n).
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%I #30 Mar 03 2018 12:50:09

%S 4,6,12,30,124,122,418,98,220,346,308,1274,1144,962,556,2512,3526,

%T 1382,1856,4618,992,3818,7432,12778,5978,26098,2642,23266,10268,19696,

%U 6008,34192,22606,5372,37768,13562,9596,22832,59914,7426,88786,50312,97768

%N a(n) = least 2k such that p is the least prime in a Goldbach partition of 2k, where p = prime(n).

%C Minimal integer m such that m=p(n)+q=sum of 2 primes, where p(n)<=q is the n-th prime and there is no prime r<p(n) such that m-r is prime. - _Robin Garcia_, Feb 12 2005

%C The increasing subsequence k(n), such that for all m>n, k(m)>k(n) is A025018, and the associated sequence of primes is A025019. - _David James Sycamore_, Feb 05 2018

%H N. J. A. Sloane, <a href="/A025017/b025017.txt">Table of n, a(n) for n = 1..977</a> (from the web page of Tomás Oliveira e Silva)

%H Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/goldbach.html">Goldbach conjecture verification</a>

%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>

%e a(4)=30=7+23 because p(4)=7, q=23 is prime and there is no prime r<p(4)=7 such that a(4)-r is prime.

%o (MATLAB) p1 = primes(1000000); d(1, :) = p1; d(2, :) = d(1, :) - d(1, :); i = 4; k = 1; n = 0; while i <= 5000000 while not(isprime(i - d(1, k))) k = k + 1; end; if d(2, k) == 0 d(2, k) = i; if k == n + 1 while d(2, n+1) > 0 n = n + 1; end; if n > 0 d(2, 1:n) end; end; end; k = 1; i = i + 2; end; - _Lei Zhou_, Jan 26 2005

%o (PARI) Gold(n)=forprime(p=2,n,if(isprime(n-p),return(p)))

%o a(n,p=prime(n))=my(k=2); while(Gold(k+=2)!=p,); k \\ _Charles R Greathouse IV_, Sep 28 2015

%Y For records see A133427, A133428.

%Y Cf. A025018, A025019.

%K nonn

%O 1,1

%A _David W. Wilson_

%E Edited by _N. J. A. Sloane_, May 05 2007; b-file added Nov 27 2007