A089296 Maximum prime required in the representation of the square of the n-th prime A000040(n) by a signed sum of squares of distinct other primes minimizing the largest prime used in the sum.

29, 37, 19, 19, 19, 19, 19, 17, 19, 19, 19, 23, 29, 29, 29, 31, 37, 37, 37, 41, 41, 43, 43, 43, 47, 47, 53, 53, 53, 53, 59, 61, 61, 61, 67, 67, 67, 71, 71, 71, 73, 73, 79, 79, 79, 79, 83, 89, 89, 89, 89, 97, 97, 97, 101, 101, 101, 101, 103, 103, 103, 103, 107, 107, 109

Offset: 1

Author

Hugo Pfoertner, Nov 18 2003

Keywords

• nonn

Examples

			a(1)=29: 2^2 = 4 = -29^2 + 19^2 + 17^2 + 11^2 + 7^2 + 5^2
a(2)=37: 3^2 = 9 = -37^2 + 23^2 + 19^2 + 17^2 + 11^2 + 7^2 + 5^2 + 2^2
a(3)=19: 5^2 = 25 = -19^2 + 17^2 + 13^2 - 11^2 + 7^2
a(4)=19: 7^2 = 49 = -19^2 + 17^2 + 11^2
		

Links

• T. Lassila, H. Pfoertner et al., Sum of unique prime squares? Thread in NG sci.math, Oct 21 2003.

Crossrefs

Cf. A089294 representation of n by distinct squares of primes, A089297 representation of (n-th prime)^2 with minimal number of terms.

Extensions

More terms from David Wasserman, Sep 01 2005