|
| |
|
|
A173081
|
|
Number of twin prime pairs < 10^n that contain at least one Ramanujan prime (A104272).
|
|
1
|
| |
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
It appears that this counts the number of Ramanujan primes < 10^n that are the lesser prime in a twin prime pair. Equivalently, this sequence also counts 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".
|
|
|
LINKS
|
Table of n, a(n) for n=1..9.
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.
|
|
|
MATHEMATICA
|
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]]]]}]
|
|
|
CROSSREFS
|
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: A163029 A045722 A047129 * A169723 A052395 A034660
Adjacent sequences: A173078 A173079 A173080 * A173082 A173083 A173084
|
|
|
KEYWORD
|
nonn,more
|
|
|
AUTHOR
|
T. D. Noe, Nov 22 2010
|
|
|
STATUS
|
approved
|
| |
|
|
