A106545 a(n) = n^2 if n^2 is the sum of two primes, otherwise a(n) = 0.

0, 4, 9, 16, 25, 36, 49, 64, 81, 100, 0, 144, 169, 196, 225, 256, 0, 324, 361, 400, 441, 484, 0, 576, 0, 676, 729, 784, 841, 900, 0, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 0, 1600, 0, 1764, 1849, 1936, 0, 2116, 2209, 2304, 2401, 2500, 0, 2704, 0, 2916, 3025

Offset: 1

Author

Alexandre Wajnberg, May 08 2005

Keywords

• easy
• nonn

Comments

For odd n, n^2 is odd so the two primes must be opposite in parity. Lesser prime must be 2 and greater prime must be n^2-2. Thus for odd n, n^2 is the sum of two primes iff n^2-2 is prime.

Examples

			a(2) = 2^2 = 4 = 2+2, a(5) = 5^2 = 25 = 23+2 (two primes).
a(1) = 0 because the sum of two primes is at least 4 and a(11) = 0 because 11^2 - 2 = 119 = 7*17 is composite.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A106544-A106548, A106562-A106564, A106571, A106573-A106575, A106577.

Programs

Mathematica

stpQ[n_]:=If[OddQ[n],PrimeQ[n^2-2],AnyTrue[n^2-Prime[Range[ PrimePi[ n^2]]], PrimeQ]]; Table[If[stpQ[n],n^2,0],{n,60}] (* The program uses the AnyTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 21 2018 *)

Formula

a(n) = n^2 - A106544(n).

Extensions

Edited and extended by Klaus Brockhaus and Ray Chandler, May 12 2005