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

1,11

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

Links

Table of n, a(n) for n=1..81.

Formula

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

Example

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.

Sequence in context: A045509 A033187 A106547 * A370512 A079842 A014756

Adjacent sequences: A106541 A106542 A106543 * A106545 A106546 A106547

Keyword

easy,nonn

Author

Alexandre Wajnberg, May 08 2005

Extensions

Extended by Ray Chandler, May 12 2005

Status

approved