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A167874
The number of distinct primes < 10^n which are members of twin-prime pairs.
0
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
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
KEYWORD
nonn
AUTHOR
Lekraj Beedassy, Nov 14 2009
EXTENSIONS
Definition rephrased by R. J. Mathar, Nov 23 2009
STATUS
approved