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A088018
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Number of twin-prime pairs between n and 2n (inclusive).
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3
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0, 0, 1, 1, 1, 0, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 6, 6, 6, 6
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,10
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COMMENTS
| To be counted, both members of the twin-prime pair must be between n and 2n, inclusive. It appears that a(n) > 0 for all n > 6. However, it has not been proved that there are an infinite number of twin primes.
Same as the number of lower twin primes between n-1 and 2(n-1), exclusive. If the twin prime conjecture is true, there are at least n lower twin primes between x/2 and x for all x >= A186312(n).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
Eric Weisstein's World of Mathematics, Twin Primes
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MATHEMATICA
| nn=100; p=Select[Prime[Range[PrimePi[2*nn]]], PrimeQ[#+2] &]; t=Table[0, {nn}]; Do[t[[Span[Ceiling[i/2], Min[nn, i-1]]]]++, {i, p}]; Prepend[t, 0]
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CROSSREFS
| Cf. A035250 (number of primes between n and 2n), A088019 (number of twin primes between n and 2n).
Sequence in context: A175078 A121561 A078772 * A204909 A099384 A015716
Adjacent sequences: A088015 A088016 A088017 * A088019 A088020 A088021
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KEYWORD
| easy,nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Sep 18 2003, Feb 17 2011
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