

A084138


a(n) is the number of times n is in sequence A060715, i.e., there are exactly a(n) cases where there are exactly n primes between m and 2m, exclusively, for m > 0.


4



1, 3, 4, 4, 7, 3, 5, 6, 2, 9, 6, 2, 5, 10, 7, 8, 5, 3, 9, 10, 6, 4, 1, 8, 6, 5, 5, 9, 11, 10, 6, 6, 10, 8, 5, 6, 1, 3, 8, 9, 9, 5, 18, 16, 5, 7, 3, 1, 3, 12, 5, 3, 3, 3, 9, 8, 16, 7, 5, 8, 15, 10, 4, 2, 8, 7, 10, 13, 17, 5, 8, 7, 9, 10, 3, 5, 3, 6, 6, 1, 6, 8, 3, 3, 10, 15, 14, 16, 7, 10, 14, 5, 5, 3, 8
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OFFSET

0,2


COMMENTS

This calculation relies on the fact that Pi(2*m)  Pi(m) > m/(3*log(m)) for m >= 5. It can be shown that a(n) is never zero, i.e., every nonnegative integer is in sequence A060715.


REFERENCES

P. Ribenboim, The Little Book of Big Primes. SpringerVerlag, 1991, p. 140.


LINKS

Table of n, a(n) for n=0..94.
Eric Weisstein's World of Mathematics, Bertrand's Postulate.


EXAMPLE

a(22)=1 because there are 22 primes between 120 and 240 (namely, prime numbers p(31)=127 through p(52)=239), and in no other case are there exactly 22 primes between m and 2m exclusively.


CROSSREFS

Cf. A060715, A060756, A084139, A084140, A084141, A084142.
Sequence in context: A325973 A019462 A078071 * A127141 A272668 A014406
Adjacent sequences: A084135 A084136 A084137 * A084139 A084140 A084141


KEYWORD

nonn


AUTHOR

Harry J. Smith, May 15 2003


STATUS

approved



