A106544 Perfect squares n^2 which are not the sum of two primes (otherwise 0).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 121, 0, 0, 0, 0, 0, 289, 0, 0, 0, 0, 0, 529, 0, 625, 0, 0, 0, 0, 0, 961, 0, 0, 0, 0, 0, 0, 0, 1521, 0, 1681, 0, 0, 0, 2025, 0, 0, 0, 0, 0, 2601, 0, 2809, 0, 0, 0, 3249, 0, 3481, 0, 0, 0, 0, 0, 4225, 0, 4489, 0, 0, 0, 0, 0, 5329, 0, 0, 0, 0, 0, 6241, 0, 6561

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. - Ray Chandler, May 12 2005

Examples

			a(10)=0 because 10^2=100=97+3 (sum of two primes)
a(11)=11^2=121, which is impossible to obtain summing two primes.
		

Crossrefs

Cf. A106545-A106548, A106562-A106564, A106571, A106573-A106575, A106577.

Formula

a(n) = n^2 - A106545(n).

Extensions

Extended by Ray Chandler, May 12 2005