A073046 - OEIS

%I #34 Dec 01 2025 18:09:05

%S 4,9,15,21,35,33,39,65,51,57,95,69,115,161,87,93,155,217,111,185,123,

%T 129,215,141,235,329,159,265,371,177,183,305,427,201,335,213,219,365,

%U 511,237,395,249,415,581,267,445,623,1501,291,485,303,309,515,321,327

%N Write 2*n = p + q (p, q prime), p*q minimal; then a(n) = p*q.

%C Least semiprime whose sum of prime factors equals 2*n.

%C Assuming Goldbach's conjecture, a(n) exists for all n >= 2. - _David James Sycamore_, Jan 08 2019

%H Reinhard Zumkeller, <a href="/A073046/b073046.txt">Table of n, a(n) for n = 2..10000</a>

%F For all n except 3, a(n) = A288814(2*n). - _David James Sycamore_, Jan 08 2019

%e n=13: 2n=26; 26 = 23 + 3 = 19 + 7 = 13 + 13; 23*3 = minimal => p*q = 23*3 = 69.

%p a:= n-> min(seq((l-> `if`(andmap(isprime, l),

%p       l[1]*l[2], [][]))([n-i, n+i]), i=0..n-2)):

%p seq(a(n), n=2..56);  # _Alois P. Heinz_, Dec 01 2025

%t Array[Block[{p = 2, q}, While[! PrimeQ@ Set[q, 2 # - p], p = NextPrime[p]]; p q] &, 55, 2] (* _Michael De Vlieger_, Aug 02 2020 *)

%o (Haskell)

%o a073046 n = head $ dropWhile (== 0) $

%o                    zipWith (*) prims $ map (a061397 . (2*n -)) prims

%o    where prims = takeWhile (<= n) a000040_list

%o -- _Reinhard Zumkeller_, Aug 28 2011

%Y Cf. A000040, A061397.

%Y Cf. A102084, A193315, A288814.

%Y Subsequence of A001358.

%K nonn

%O 2,1

%A _Werner D. Sand_, Aug 31 2002

%E Corrected by _Ray Chandler_, Jun 11 2005