Search: id:A061265
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%I A061265
%S A061265 0,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,1,0,
%T A061265 0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,
%U A061265 0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,1
%N A061265 Number of squares between n-th prime and (n+1)st prime.
%C A061265 If n-th prime is a member of A053001 then a(n) is at least 1. If not, 
               then a(n) = 0.
%C A061265 Legendre's conjecture (still open) that there is always a prime between 
               n^2 and (n+1)^2 is equivalent to conjecturing that a(n)<=1 for all 
               n. - Vladeta Jovovic (vladeta(AT)eunet.rs), May 01 2003
%H A061265 Harry J. Smith, <a href="b061265.txt">Table of n, a(n) for n=1,...,2000</
               a>
%F A061265 a(n) = floor(sqrt(prime(n+1)))-floor(sqrt(prime(n))). - Vladeta Jovovic 
               (vladeta(AT)eunet.rs), May 01 2003
%e A061265 a(3) = 0 as there is no square between 5, the third prime and 7, the 
               fourth prime. a(4) = 1, as there is a square '9' between the 4th 
               prime 7 and the 5th prime 11.
%o A061265 (PARI) { n=0; q=2; forprime (p=3, prime(2001), write("b061265.txt", n++, 
               " ", floor(sqrt(p))-floor(sqrt(q))); q=p ) } [From Harry J. Smith 
               (hjsmithh(AT)sbcglobal.net), Jul 20 2009]
%Y A061265 Cf. A053001.
%Y A061265 Cf. A038107.
%Y A061265 Sequence in context: A082848 A141743 A112416 this_sequence A125122 A000035 
               A131734
%Y A061265 Adjacent sequences: A061262 A061263 A061264 this_sequence A061266 A061267 
               A061268
%K A061265 nonn,base
%O A061265 1,1
%A A061265 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 24 2001
%E A061265 Extended by Patrick De Geest (pdg(AT)worldofnumbers.com), Jun 05 2001.
%E A061265 OFFSET changed from 0,1 to 1,1 by Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Jul 20 2009

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