|
%I #22 Oct 02 2014 23:15:44
%S 2,4,6,6,10,8,14,8,18,12,22,10,26,16,30,10,34,12,38,14,42,24,46,12,50,
%T 28,54,18,58,16,62,12,66,36,70,14,74,40,78,16,82,20,86,26,90,48,94,14,
%U 98,20,102,30,106,24,110,20,114,60,118,18,122,64,126,14,130
%N Write 2n as a product of numbers of the form 4k+2 (A016825) so as to minimize the sum of the factors; a(n) is this sum.
%C Suggested by reading Joshua Zucker's puzzle in Gary Antonick's Numberplay column for April 22 2013. Sequence A016825 gives the "primes" (the irreducible elements) in Evenland.
%H Jens Kruse Andersen, <a href="/A247653/b247653.txt">Table of n, a(n) for n = 1..10000</a>
%H Gary Antonick, <a href="http://wordplay.blogs.nytimes.com/2013/04/22/evenland">The Primes in Evenland Puzzle</a>, Numberplay Column, Wordplay Blog, New York Times, April 22, 2013
%e 20 = 2*10 so a(10) = 2+10 = 12.
%e The first time there is a choice is when n=18: 36 = 2*18 = 6*6, and the latter gives the smaller sum, so a(18) = 6+6 = 12.
%o (PARI) f(x,i)=local(t); if(x==1, 0, if(i>#d, 2^99, t=f(x, i+1); if(x%d[i], t, min(t, d[i]+f(x/d[i], i)))))
%o a(n)=d=select(m->m%4==2, divisors(2*n)); f(2*n, 1) \\ _Jens Kruse Andersen_, Oct 01 2014
%Y Cf. A016825, A247654, A001414.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Sep 30 2014
%E Definition corrected and more terms from _Jens Kruse Andersen_, Oct 01 2014
|
