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Search: id:A065978
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| A065978 |
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For even n>=4, let f(n)=A066285(n/2) be the minimal difference between primes p and q whose sum is n. Such an n is in the sequence if f(n)>f(m) for all even m with 4<=m<n. |
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4
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| 4, 8, 16, 44, 92, 242, 256, 272, 292, 476, 530, 572, 682, 688, 1052, 1808, 2228, 3382, 3472, 3502, 3562, 4952, 6194, 7102, 10262, 17008, 20684, 37052, 45128, 49552, 80144, 137414, 251806, 349826, 362534, 742856, 1655152, 1872236, 2108282, 2319728, 2707118, 5182214, 7518328, 10908124, 11939162, 12727966, 13279472, 13583338, 14366372, 18245438, 21572990, 47697614, 54144704, 92661736, 115978712, 366468878
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OFFSET
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0,1
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COMMENT
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The values of f(a(n)) (given in A066286) appear to be divisible by 6, except the first two.
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EXAMPLE
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E.g. 4=2+2, the gap is 0. 6=3+3 (0), 8=3+5, the gap is 2, this is the largest gap to date and so 8 is in the sequence. 10=5+5 (0), 12=5+7(2), 14=7+7(0), 16=5+11(6), so 16 is in the sequence.
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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-2p]]]; For[n=4; max=-1, True, n+=2, If[f[n]>max, Print[n]; max=f[n]]]
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CROSSREFS
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Cf. A066285, A066286.
Sequence in context: A141069 A144687 A065605 this_sequence A077447 A102358 A038238
Adjacent sequences: A065975 A065976 A065977 this_sequence A065979 A065980 A065981
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KEYWORD
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nonn,nice
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Dec 09 2001
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) and Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 10 2001
a(51)-a(55) from Gilmar Rodriguez (Gilmar.Rodriguez(AT)nwfwmd.state.fl.us), Jun 16 2005. a(56) from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 27 2005.
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