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Search: id:A107926
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| A107926 |
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Consider the Goldbach problem and the minimal difference between two primes p&q with n=p+q=a(p-q). This sequence is the least even number n with this property. |
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2
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| 4, 8, 18, 16, 54, 48, 50, 108, 102, 44, 234, 444, 98, 228, 174, 92, 414, 432, 242, 516, 582, 256, 1182, 672, 406, 612, 846, 272, 1038, 984, 442, 1776, 1902, 292, 1074, 636, 1054, 3312, 1122, 476, 1398, 1464, 530, 1728, 2730, 572, 2706, 3348, 682, 2844, 3342
(list; graph; listen)
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OFFSET
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0,1
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LINKS
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Mark Herkommer, Goldbach Conjecture Research.
NationMaster.com, Goldbach's-conjecture.
Tomas Oliveira e Silva, Goldbach conjecture verification.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics..
Wikipedia, the free encyclopedia, Goldbach conjecture.
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EXAMPLE
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a(1)=8 because the difference between 5&3=2 and 8 is the least number having this property.
a(2)=18 because 18=5+13=7+11, and the pair 7&11 have the lesser difference of 4.
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MATHEMATICA
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f[n_] := For[p = n/2, True, p--, If[PrimeQ[p] && PrimeQ[n - p], Return[n/2 - p]]]; t = Table[0, {100}]; Do[ d = f[2n]; If[ t[[d + 1]] == 0, t[[d + 1]] = n; Print[{d, 2n}]], {n, 2, 1700}]; 2Take[t, 52]]
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CROSSREFS
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Cf. A066285, records in A065978 & A066286.
Sequence in context: A119471 A075558 A110601 this_sequence A070213 A077474 A009918
Adjacent sequences: A107923 A107924 A107925 this_sequence A107927 A107928 A107929
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KEYWORD
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nonn
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AUTHOR
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Gilmar J. Rodriguez (Gilmar.Rodriguez(AT)nwfwmd.state.fl.us) and Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 16 2005
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