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A200778
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Least k >0 such that k*p*(k*p-1)-1 and k*p*(k*p-1)+1 is a twin prime pair, where p=prime(n).
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2
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2, 1, 5, 1, 2, 3, 3, 13, 9, 8, 10, 43, 69, 15, 17, 50, 3, 42, 1, 2, 3, 3, 20, 33, 3, 44, 7, 35, 49, 9, 6, 189, 15, 1, 113, 21, 7, 154, 3, 3, 18, 12, 29, 33, 20, 6, 27, 3, 2, 3, 23, 11, 10, 12, 18, 137, 41, 12, 36, 29, 54, 17, 10, 59, 55, 3, 51, 36
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OFFSET
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1,1
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COMMENTS
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lim_{N->infinity) (Sum_{n=1..N} k(n)) / (Sum_{n=1..N} log(p(n))^2) = 1.
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LINKS
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EXAMPLE
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2*2*(2*2 - 1) - 1 = 11, twin prime of 13, so a(1)=2.
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MAPLE
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p := ithprime(n) ;
for k from 1 do
if isprime(k*p*(k*p-1)-1) and isprime(k*p*(k*p-1)+1) then
return k;
end if;
end do:
end proc:
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MATHEMATICA
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lktpp[n_]:=Module[{k=1, p=Prime[n]}, While[AnyTrue[k*p(k*p-1)+{1, -1}, CompositeQ], k++]; k]; Array[lktpp, 70] (* Harvey P. Dale, May 03 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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