A089297 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 number of terms in the sum.

29, 37, 19, 19, 19, 31, 19, 17, 19, 23, 29, 31, 31, 37, 37, 47, 43, 47, 53, 59, 59, 59, 71, 67, 71, 73, 79, 79, 83, 83, 97, 97, 101, 101, 109, 109, 127, 127, 127, 137, 139, 131, 149, 139, 151, 149, 163, 167, 191, 173, 167, 179, 179, 191, 191, 193, 193, 193, 199, 211

Offset: 1

Author

Hugo Pfoertner, Nov 18 2003

Keywords

• nonn

Comments

a(1) requires 6 squares, a(2) requires 8, a(3) requires 5 and a(4) through a(70) require 3. - David Wasserman, Sep 01 2005

Examples

			The first representations different from those in A089296 are
a(6)=31: 13^2 = 169 = 31^2 - 29^2 + 7^2 = -31^2 + 29^2 + 17^2
a(10)=23: 29^2 = 841 = 23^2 + 19^2 - 7^2
a(11)=29: 31^2 = 961 = 29^2 + 13^2 - 7^2
		

Links

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

Crossrefs

Cf. A088934 representation of n by distinct squares of primes, A089296 representation of (n-th prime)^2 with maximum term minimized.

Extensions

More terms from David Wasserman, Sep 01 2005