

A025017


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


7



4, 6, 12, 30, 124, 122, 418, 98, 220, 346, 308, 1274, 1144, 962, 556, 2512, 3526, 1382, 1856, 4618, 992, 3818, 7432, 12778, 5978, 26098, 2642, 23266, 10268, 19696, 6008, 34192, 22606, 5372, 37768, 13562, 9596, 22832, 59914, 7426, 88786, 50312, 97768
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OFFSET

1,1


COMMENTS

Minimal integer m such that m=p(n)+q=sum of 2 primes, where p(n)<=q is the nth prime and there is no prime r<p(n) such that mr is prime.  Robin Garcia, Feb 12 2005
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


LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..977 (from the web page of Tomás Oliveira e Silva)
Tomás Oliveira e Silva, Goldbach conjecture verification
Index entries for sequences related to Goldbach conjecture


EXAMPLE

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.


PROG

(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
(PARI) Gold(n)=forprime(p=2, n, if(isprime(np), return(p)))
a(n, p=prime(n))=my(k=2); while(Gold(k+=2)!=p, ); k \\ Charles R Greathouse IV, Sep 28 2015


CROSSREFS

For records see A133427, A133428.
Cf. A025018, A025019.
Sequence in context: A178674 A025018 A102043 * A133427 A027070 A087785
Adjacent sequences: A025014 A025015 A025016 * A025018 A025019 A025020


KEYWORD

nonn


AUTHOR

David W. Wilson


EXTENSIONS

Edited by N. J. A. Sloane, May 05 2007; bfile added Nov 27 2007


STATUS

approved



