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Largest k such that there are exactly n primes between k^2 and (k+1)^2.
5

%I #9 Apr 29 2012 22:33:33

%S 5,9,14,17,23,26,30,42,49,55,56,80,77,72,85,84,89,119,102,118,137,136,

%T 143,140,149,156,174,178,188,184,194,200,195,207,219,198,228,247,261,

%U 263,245,249,279,297,289,327,306,310,325,335,321,290,356,344,425,365

%N Largest k such that there are exactly n primes between k^2 and (k+1)^2.

%C a(n) is the index of last occurrence of n in A014085. This sequence relies on a heuristic calculation and there is no proof that it is correct. Conjecture: There is no k that has only one prime between k^2 and (k+1)^2.

%D P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 143.

%H T. D. Noe, <a href="/A084597/b084597.txt">Table of n, a(n) for n = 2..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LandausProblems.html">Landau's Problems</a>.

%e a(14)=77 because 14 is in sequence A014085 for the last time at item 77. There are 14 primes between 77^2 and 78^2.

%Y Cf. A007491, A014085, A076957, A084596.

%K nonn

%O 2,1

%A _Harry J. Smith_, May 31 2003