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A212595
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Let f(n) = 2n-7. Difference between f(n) and the nearest prime < f(n).
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1
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2, 2, 4, 2, 2, 4, 2, 4, 6, 2, 2, 4, 6, 2, 4, 2, 2, 4, 2, 4, 6, 2, 4, 6, 2, 2, 4, 6, 2, 4, 2, 2, 4, 6, 2, 4, 2, 4, 6, 2, 4, 6, 8, 2, 4, 2, 2, 4, 2, 2, 4, 2, 4, 6, 8, 10, 12, 14, 2, 4, 2, 4, 6, 2, 2, 4, 6, 8, 10, 2, 2, 4, 6, 2, 4, 6, 2, 4, 2, 4, 6, 2, 4, 6, 2, 2
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OFFSET
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10,1
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COMMENTS
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It's known that there is always a prime between n and 2n - 7 for all n >= 10.
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LINKS
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EXAMPLE
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a(12) = 4 because 2*12-7 = 17, and the nearest prime p < 17 such that 12 < p < 17 is p = 13. Hence a(12) = 17 - 13 = 4.
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MAPLE
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with(numtheory):for n from 10 to 100 do:x:=2*n-7:i:=0:for p from x-1 by -1 to n+1 while(i=0) do:if type(p, prime)=true then i:=1:printf(`%d, `, x-p):else fi:od:od:
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MATHEMATICA
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Array[# - Prime@ PrimePi[# - 1] &[2 # - 7] &, 86, 10] (* Michael De Vlieger, Oct 17 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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