

A162309


a(n) is the number of isolated primes up to the smaller component of the nth twin prime pair.


1



1, 1, 1, 1, 2, 3, 5, 6, 10, 10, 13, 13, 17, 17, 17, 19, 20, 23, 24, 26, 29, 39, 39, 43, 50, 54, 57, 59, 60, 62, 80, 80, 80, 82, 84, 101, 101, 102, 102, 104, 110, 119, 122, 123, 124, 125, 133, 136, 138, 138, 153, 154, 158, 159, 160, 167, 174, 174, 178, 178, 182, 185, 189, 189
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OFFSET

1,5


COMMENTS

Cardinality of the set of terms of A007510 which are smaller than A001359(n).


LINKS

Table of n, a(n) for n=1..64.


FORMULA

a(n+1)  a(n) = A027833(n)  2, n > 1. [R. J. Mathar, Aug 29 2009]


EXAMPLE

a(1)=1 counts the isolated prime 2, which smaller than 3;
a(2)=1 counts the isolated prime 2, which is smaller than 5;
a(5)=2 counts the isolated primes 2 and 23, which are smaller than 29;
a(6)=3 counts 2, 23 and 37, which are smaller than 41.


MAPLE

read("transforms3") ; tp := BFILETOLIST("b001359.txt") ;
A162309 := proc(n) global tp; a := 0 ; for j from 2 to op(n, tp)1 do if isprime(j) then if ( j in tp ) or (j2) in tp then ; else a :=a +1; fi; fi; od: a ; end:
seq(A162309(n), n=1..130 ); # R. J. Mathar, Aug 29 2009


CROSSREFS

Cf. A000040, A141468, A073425.
Sequence in context: A061939 A029503 A133139 * A014593 A261088 A303431
Adjacent sequences: A162306 A162307 A162308 * A162310 A162311 A162312


KEYWORD

nonn


AUTHOR

JuriStepan Gerasimov, Jul 01 2009


EXTENSIONS

53 replaced with 54, 100 removed twice, etc., by R. J. Mathar, Aug 29 2009


STATUS

approved



