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%I M4080 #17 May 13 2013 01:54:03
%S 6,9,27,45,45,57,75,81,87,105,123,135,135,165,169,189,195,209,231,237,
%T 267,267,267,315,315,333,345,363,369,405,411,429,441,465,483,485,525,
%U 525,535,555,579,579,609,611,645,657,687,705,715,717,721
%N Largest number not a sum of distinct primes >= prime(n).
%C Kløve conjectures that a(n) ~ 3p where p is the n-th prime. This implies the (binary) Goldbach conjecture for large enough n. - _Charles R Greathouse IV_, Apr 03 2012
%D Torleiv Kløve, Sums of distinct primes. Nordisk Mat. Tidskr. 21 (1973), pp. 138-140.
%D J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 73.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Charles R Greathouse IV, <a href="/A007414/b007414.txt">Table of n, a(n) for n = 1..10000</a>
%o (PARI) issum(n,x)=if(isprime(n),return(n>=x));if(if(n%2, n<3*x, n<2*x), return(!n));forprime(p=x,n-if(n%2,2*x,x),if(issum(n-p,p+1),return(1)));0
%o a(n)=my(p=prime(n),k=2*p-2,lower=k,upper=2*k+2);while(upper>lower, if(issum(upper,p),upper--,lower=2*k+2;k=upper;upper=2*k+2));k \\ _Charles R Greathouse IV_, Apr 03 2012
%Y Cf. A180306.
%K nonn
%O 1,1
%A _N. J. A. Sloane_.
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