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%I #18 Feb 13 2015 02:17:54
%S 0,3,7,11,23,19,23,47,31,35,71,43,87,131,55,59,119,179,71,143,79,83,
%T 167,91,183,275,103,207,311,115,119,239,359,131,263,139,143,287,431,
%U 155,311,163,327,491,175,351,527,1403,191,383,199,203,407,211,215,431,223,447,671
%N Let 2n = p + q where p and q are primes. Take the p and q that produce the smallest product, then set a(n) = p*q - 2n.
%C Trying to translate the Goldbach conjecture into multiplication.
%H Isaac E. Lambert and Charles R Greathouse IV, <a href="/A137516/b137516.txt">Table of n, a(n) for n = 2..10000</a> (first 100 terms from Lambert)
%e For example, the 13th term of the sequence is 43 since 26 = 3 + 23 (and the product 69 is minimal) and 3*23 - 26 = 43.
%t f[n_] := Block[{p = 2}, While[ !PrimeQ[ 2n - p], p = NextPrime@ p]; 2n(p - 1) - p^2]; Array[f, 59, 2] (* _Robert G. Wilson v_, Mar 25 2012 *)
%o (PARI) a(n)=n+=n;forprime(p=2,default(primelimit),if(isprime(n-p),return(p*n-p^2-n))) \\ _Charles R Greathouse IV_, Mar 26 2012
%K nonn,easy
%O 2,2
%A _Isaac Lambert_, Apr 23 2008
%E Edited by _N. J. A. Sloane_, May 23 2008
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