%I #16 Apr 16 2013 15:40:52

%S 1,7,12,26,49,55,106,106,163,229,229,307,343,343,394,458,655,655,655,

%T 655,758,812,1358,1472,1472,1472,1618,1618,1767,2058,2191,2191,2393,

%U 2638,2916,3108,3108,3339,3437,3946,4272,4353,4353,5107,5107,5523,5523,5744

%N a(n) = smallest k such that there is no square between prime(k) and prime(k+n).

%C The sequence is apparently infinite.

%H Zak Seidov, <a href="/A224699/b224699.txt">Table of n, a(n) for n = 1..2000</a>

%e a(2000) = 19907242 because p = prime(19907242) = 371756971, q = prime(19907242 + 2000) = 371795461, and between p anq q there is no square: (19281^2 = 371756961) < p and (19282^2 = 371795524) > q.

%t m1 = 1; s = {}; Do[Do[If[Ceiling[Sqrt[Prime[m]]]^2 > Prime[m + k], AppendTo[s, m]; m1 = m; Break[]], {m, m1, 10^6}], {k, 60}]; s

%Y Cf. A221056.

%K nonn

%O 1,2

%A _Zak Seidov_, Apr 16 2013