A109270 Numbers n such that n^2 > (1/2)(prevprime(n^2)+nextprime(n^2)).

4, 6, 10, 11, 14, 16, 17, 20, 22, 24, 26, 28, 30, 31, 36, 38, 39, 40, 45, 48, 50, 52, 54, 56, 57, 59, 62, 65, 66, 67, 70, 73, 74, 76, 79, 81, 84, 85, 87, 90, 91, 94, 95, 96, 97, 99, 100, 104, 105, 106, 109, 110, 111, 114, 115, 116, 120, 122, 123, 124, 125, 126, 130, 134

Offset

1,1

Comments

One may call these n^2 the "strong squares" by analogy with A051634 (Strong primes).

Links

Table of n, a(n) for n=1..64.

Example

4^2=16>(13+17)/2 so 4 is a term;
5^2 < (23+29)/2=26, so 5 is not a term;
6^2=36>(31+37)/2 so 6 is a term, etc.

Maple

a:=proc(n) if n^2 > (1/2)*(prevprime(n^2)+nextprime(n^2)) then n else fi end: seq(a(n), n=2..150); # Emeric Deutsch, Jun 26 2005

Mathematica

prQ[n_]:=Module[{n2=n^2}, n2>(NextPrime[n2]+NextPrime[n2, -1])/2]; Select[ Range[2, 150], prQ] (* Harvey P. Dale, Feb 19 2012 *)

Crossrefs

Cf. A051634, A033597, A075190, A109269. The interprimes (the average of two consecutive odd primes) are in A024675.

Sequence in context: A141780 A185002 A110604 * A187331 A184923 A137877

Adjacent sequences: A109267 A109268 A109269 * A109271 A109272 A109273

Keyword

nonn

Author

Zak Seidov, Jun 24 2005

Extensions

More terms from Emeric Deutsch, Jun 26 2005

Status

approved