A137516 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.

0, 3, 7, 11, 23, 19, 23, 47, 31, 35, 71, 43, 87, 131, 55, 59, 119, 179, 71, 143, 79, 83, 167, 91, 183, 275, 103, 207, 311, 115, 119, 239, 359, 131, 263, 139, 143, 287, 431, 155, 311, 163, 327, 491, 175, 351, 527, 1403, 191, 383, 199, 203, 407, 211, 215, 431, 223, 447, 671

Offset: 2

Author

Isaac Lambert, Apr 23 2008

Keywords

• nonn
• easy

Comments

Trying to translate the Goldbach conjecture into multiplication.

Examples

			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.
		

Links

• Isaac E. Lambert and Charles R Greathouse IV, Table of n, a(n) for n = 2..10000 (first 100 terms from Lambert)

Programs

Mathematica

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 *)

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

Extensions

Edited by N. J. A. Sloane, May 23 2008