A088908 -id:A088908 - cp's OEIS frontend

A088909 Numbers expressible as the sum of squares of two distinct primes.

13, 29, 34, 53, 58, 74, 125, 130, 146, 170, 173, 178, 194, 218, 290, 293, 298, 314, 338, 365, 370, 386, 410, 458, 482, 530, 533, 538, 554, 578, 650, 698, 818, 845, 850, 866, 890, 962, 965, 970, 986, 1010, 1082, 1130, 1202, 1250, 1322, 1370, 1373, 1378, 1394

Offset: 1

Hugo Pfoertner, Oct 22 2003

nonn

			a(1)=3*3+2*2=13, a(2)=5*5+2*2=29.

Cf. A001481, A088908.

Union[Total/@(Subsets[Prime[Range[20]],{2}]^2)] (* Harvey P. Dale, Nov 16 2013 *)

A088910 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.

Original entry on oeis.org

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, 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, 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

Offset: 0

Hugo Pfoertner, Oct 24 2003

nonn

It is conjectured that all sequence terms are <=5. The terms with a(n)=5 were provided by W. Edwin Clark.

			The following are representation with the minimal number of terms:
  a(0)=4: 0=7^2-11^2-17^2+19^2;
  a(1)=3: 1=7^2+11^2-13^2;
  a(4)=1: 4=2^2;
  a(5)=2: 5=3^2-2^2;
  a(6)=5: 6=-(2^2)+3^2+7^2+11^2-13^2.

Robert E. Dressler, Louis Pigno, and Robert Young, Sums of squares of primes, Nordisk Mat. Tidskr. 24 (1976), 39-40.
Hugo Pfoertner, Conjectured minimal representations of n by squaresof distinct primes (Table for n<=400).

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

cp's OEIS Frontend

A088909 Numbers expressible as the sum of squares of two distinct primes.

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