A224699 a(n) = smallest k such that there is no square between prime(k) and prime(k+n).

1, 7, 12, 26, 49, 55, 106, 106, 163, 229, 229, 307, 343, 343, 394, 458, 655, 655, 655, 655, 758, 812, 1358, 1472, 1472, 1472, 1618, 1618, 1767, 2058, 2191, 2191, 2393, 2638, 2916, 3108, 3108, 3339, 3437, 3946, 4272, 4353, 4353, 5107, 5107, 5523, 5523, 5744

Offset: 1

Author

Zak Seidov, Apr 16 2013

Keywords

• nonn

Comments

The sequence is apparently infinite.

Examples

			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.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A221056.

Programs

Mathematica

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