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Search: id:A161562
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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
1
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| 2, 4, 6, 8, 10, 16, 18, 20, 22, 24, 36, 60, 84, 90, 114, 120, 210, 420
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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
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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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PROGRAM
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(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
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Sequence in context: A113293 A080431 A122642 this_sequence A102470 A057195 A088007
Adjacent sequences: A161559 A161560 A161561 this_sequence A161563 A161564 A161565
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KEYWORD
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nonn,fini,full,new
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 13 2009
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EXTENSIONS
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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 (mhasler(AT)univ-ag.fr), Nov 11 2009
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