%I A084142
%S A084142 1,120,216,300,531,714,804,999,1344,1356,1395,1680,1764,1770,1959,2046,
%T A084142 2121,2325,2484,2511,2760,2826,3150,3285,3396,3744,4044,4116,4146,4314,
%U A084142 4710,4839,5046,5070,5136,5250,5586,5970,6411,6459,6501,6504,6846,7275
%N A084142 There are a unique number of primes between a(n) and 2a(n). This is a 
               list of all such integers > zero in numerical order.
%C A084142 The number of primes between a(n) and 2a(n) is unique because no other 
               number m has the same of primes between m and 2m, exclusively, for 
               m>0. a(n) is the value of A060756 or A084139 when A084138 is one. 
               Question: Is this sequence infinitely long?
%D A084142 P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 
               140.
%H A084142 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               BertrandsPostulate.html">Link to a section of The World of Mathematics.</
               a> Bertrand's Postulate.
%e A084142 The number 120 is in the list because there are 22 primes between 120 
               and 240
%e A084142 and no other number m has 22 primes between m and 2m, m>0.
%Y A084142 Cf. A060715, A060756, A084138, A084139, A084140, A084141.
%Y A084142 Sequence in context: A069674 A003015 A098565 this_sequence A146950 A028976 
               A158130
%Y A084142 Adjacent sequences: A084139 A084140 A084141 this_sequence A084143 A084144 
               A084145
%K A084142 nonn
%O A084142 0,2
%A A084142 Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 15 2003