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A173081
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Number of twin prime pairs < 10^n that contain at least one Ramanujan prime (A104272).
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1
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0, 6, 28, 167, 964, 6305, 45082, 335919, 2605867, 20841010, 170395131
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OFFSET
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1,2
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COMMENTS
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It appears that this gives the number of Ramanujan primes < 10^n that are the lesser prime in a twin prime pair. Equivalently, this sequence also gives the number of Ramanujan primes p with p+2 also prime less than 10^n.
It appears that no upper twin prime is a Ramanujan prime without the corresponding lower twin prime also being a Ramanujan prime.
This is proved in Section 4 of "Ramanujan Primes: Bounds, Runs, Twins, and Gaps".
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LINKS
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Table of n, a(n) for n=1..11.
J. Sondow, J. W. Nicholson, and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, J. Integer Seq. 14 (2011) Article 11.6.2.
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MATHEMATICA
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nn=50000; t=Table[0, {nn}]; s=0; Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s<nn, t[[s+1]]=k], {k, Prime[3*nn]}]; t=t+1; cnt=0; i=1; Table[While[t[[i]]<10^n, If[PrimeQ[t[[i]]+2], cnt++]; i++]; cnt, {n, Floor[Log[10, t[[-1]]]]}]
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CROSSREFS
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Cf. A178128 (Ramanujan primes p such that p+2 is prime), A007508 (number of twin primes pairs < 10^n), A181678 (number of twin Ramanujan primes pairs < 10^n).
Sequence in context: A344755 A045722 A047129 * A278015 A338810 A345002
Adjacent sequences: A173078 A173079 A173080 * A173082 A173083 A173084
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KEYWORD
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nonn,more
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AUTHOR
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T. D. Noe, Nov 22 2010
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EXTENSIONS
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a(10)-a(11) from Dana Jacobsen, Apr 29 2015
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STATUS
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approved
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