A088910 - OEIS

%I #8 Mar 25 2022 10:38:50

%S 4,3,4,4,1,2,5,5,4,1,4,4,3,2,4,3,2,5,5,4,3,2,4,3,2,1,4,4,3,2,3,5,4,3,

%T 2,4,3,4,3,3,2,5,5,4,3,2,4,3,2,1,4,4,3,2,3,5,4,3,2,4,5,4,3,3,4,3,5,4,

%U 3,4,3,3,2,3,2,4,3,4,3,4,4,3,4,3,5,4,4,3,4,5,5,4,3,4,4,3,2,3,4,4,3,4,5,5,4

%N Conjectured minimal required number k of terms in a representation n=sum_(i=1..k)e_i*(p_i)^2 by distinct primes p_i, where e_i is 1 or -1.

%C It is conjectured that all sequence terms are <=5. The terms with a(n)=5 were provided by _W. Edwin Clark_.

%H Robert E. Dressler, Louis Pigno, and Robert Young, <a href="http://www.jstor.org/stable/43774462">Sums of squares of primes</a>, Nordisk Mat. Tidskr. 24 (1976), 39-40.

%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a088910.txt">Conjectured minimal representations of n by squaresof distinct primes</a> (Table for n<=400).

%e The following are representation with the minimal number of terms:

%e   a(0)=4: 0=7^2-11^2-17^2+19^2;

%e   a(1)=3: 1=7^2+11^2-13^2;

%e   a(4)=1: 4=2^2;

%e   a(5)=2: 5=3^2-2^2;

%e   a(6)=5: 6=-(2^2)+3^2+7^2+11^2-13^2.

%Y Cf. A088934 (maximum required prime in representation), A048261, A088908, A088909.

%K nonn

%O 0,1

%A _Hugo Pfoertner_, Oct 24 2003