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

1,1

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

Links

Table of n, a(n) for n=1..60.

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

Example

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

Crossrefs

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

Sequence in context: A172413 A134254 A089296 * A250291 A127956 A347038

Adjacent sequences: A089294 A089295 A089296 * A089298 A089299 A089300

Keyword

nonn

Author

Hugo Pfoertner, Nov 18 2003

Extensions

More terms from David Wasserman, Sep 01 2005

Status

approved