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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
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A359362 A056942 A115947 * A061228 A070229 A248835
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

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Last modified July 21 21:50 EDT 2024. Contains 374475 sequences. (Running on oeis4.)