cp's OEIS Frontend

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.

%I A089297 #8 Mar 31 2012 13:20:51
%S A089297 29,37,19,19,19,31,19,17,19,23,29,31,31,37,37,47,43,47,53,59,59,59,71,
%T A089297 67,71,73,79,79,83,83,97,97,101,101,109,109,127,127,127,137,139,131,
%U A089297 149,139,151,149,163,167,191,173,167,179,179,191,191,193,193,193,199,211
%N 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.
%C A089297 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
%H A089297 T. Lassila, H. Pfoertner et al., <a href="http://groups.google.com/group/sci.math/browse_thread/thread/78e4c851ebdb9280/d8a1aed3599aefe8">Sum of unique prime squares?</a> Thread in NG sci.math, Oct 21 2003.
%e A089297 The first representations different from those in A089296 are
%e A089297 a(6)=31: 13^2 = 169 = 31^2 - 29^2 + 7^2 = -31^2 + 29^2 + 17^2
%e A089297 a(10)=23: 29^2 = 841 = 23^2 + 19^2 - 7^2
%e A089297 a(11)=29: 31^2 = 961 = 29^2 + 13^2 - 7^2
%Y A089297 Cf. A088934 representation of n by distinct squares of primes, A089296 representation of (n-th prime)^2 with maximum term minimized.
%K A089297 nonn
%O A089297 1,1
%A A089297 _Hugo Pfoertner_, Nov 18 2003
%E A089297 More terms from _David Wasserman_, Sep 01 2005