A247653 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.

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, 28, 54, 18, 58, 16, 62, 12, 66, 36, 70, 14, 74, 40, 78, 16, 82, 20, 86, 26, 90, 48, 94, 14, 98, 20, 102, 30, 106, 24, 110, 20, 114, 60, 118, 18, 122, 64, 126, 14, 130

Offset

1,1

Comments

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.

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Gary Antonick, The Primes in Evenland Puzzle, Numberplay Column, Wordplay Blog, New York Times, April 22, 2013

Example

20 = 2*10 so a(10) = 2+10 = 12.
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.

Prog

(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)))))
a(n)=d=select(m->m%4==2, divisors(2*n)); f(2*n, 1) \\ Jens Kruse Andersen, Oct 01 2014

Crossrefs

Cf. A016825, A247654, A001414.

Sequence in context: A359362 A056942 A115947 * A061228 A070229 A248835

Adjacent sequences: A247650 A247651 A247652 * A247654 A247655 A247656

Keyword

nonn

Author

N. J. A. Sloane, Sep 30 2014

Extensions

Definition corrected and more terms from Jens Kruse Andersen, Oct 01 2014

Status

approved