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A161562
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Even numbers n such that { n-p ; p prime, 2 < p < n/2 } contains at least twice as much primes than composites.
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0
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2, 4, 6, 8, 10, 16, 18, 20, 22, 24, 36, 60, 84, 90, 114, 120, 210, 420
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The Mmca code does not produce the terms 2,4,6,8,10: For these terms there is no composite in the set { n-p }, such that the ratio (#primes)/(#composites) is not defined. For all numbers > 10 there are at least two primes and one composite in this set.
It seems that this sequence is finite, and that 420 is the largest term. [M. F. Hasler, Nov 11 2009]
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MATHEMATICA
| lst={}; Do[x=y=0; Do[If[2*Prime[k]>=n, Break[]]; If[PrimeQ[n-Prime[k]], x++, y++ ], {k, 2, 7!}]; If[x==0, x=1]; If[y==0, y=1]; If[x/y>=2, AppendTo[lst, n]], {n, 10, 6!, 2}]; lst
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PROG
| (PARI) {for(n=1, 1e6, my(s=0); forprime( p=3, n-1, s+=if( isprime(2*n-p), 1, -2)); s>=0 & print1(2*n", "))} \\ [M. F. Hasler, Nov 11 2009]
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CROSSREFS
| Sequence in context: A080431 A122642 A177867 * A102470 A057195 A088007
Adjacent sequences: A161559 A161560 A161561 * A161563 A161564 A161565
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KEYWORD
| nonn,fini,full
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AUTHOR
| Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 13 2009
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EXTENSIONS
| 16-3=13,16-5=11.(primes:2 times) 16-7=9.(composite:1 time), 24-5=19,24-7=17,24-11=13.(primes:3 times) 24-3=21.(composite:1 time), 90-3=87,90-7=83,90-11=79,90-17=73,90-19-71,90-23=67,90-29=61,90-31=59,90-37=53,90-43=47.(primes:10 times) 90-5=85,90-13=77,90-41=49.(composite:3 times),..
Reworded definition, added intitial terms & PARI code M. F. Hasler (www.univ-ag.fr/~mhasler), Nov 11 2009
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