A167874 The number of distinct primes < 10^n which are members of twin-prime pairs.

3, 15, 69, 409, 2447, 16337, 117959, 880623, 6849011, 54825357, 448752095, 3741170439, 31669329743, 271560643329, 2354418484607, 20608371394595, 181897678706317, 1617351777154871

Offset

1,1

Comments

Number of terms in A001097 with at most n digits.

The entries are odd because 5 is counted only once, although it is a member of two twin prime pairs, (3,5) and (5,7).

Cardinality of the set of {A001359 U A006512} with entries < 10^n. - R. J. Mathar, Nov 23 2009

Links

Table of n, a(n) for n=1..18.

Formula

a(n) = 2*A007508(n) - 1.

Example

There are exactly a(2) = 15 distinct primes below 10^2 that form twin primes (p, p+2), namely,
3, 5, 7, 11, 13, 17, 19, 29, 31, 41, 43, 59, 61, 71, 73 :
(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73).

Crossrefs

Cf. A001097, A077800, A007508.

Sequence in context: A224749 A122558 A110211 * A318967 A277370 A213140

Adjacent sequences: A167871 A167872 A167873 * A167875 A167876 A167877

Keyword

nonn

Author

Lekraj Beedassy, Nov 14 2009

Extensions

Definition rephrased by R. J. Mathar, Nov 23 2009

Status

approved