A088909 -id:A088909 - cp's OEIS frontend

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.

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.

A088908 Numbers expressible as sum or difference of the squares of two distinct primes.

Original entry on oeis.org

5, 13, 16, 21, 24, 29, 34, 40, 45, 48, 53, 58, 72, 74, 96, 112, 117, 120, 125, 130, 144, 146, 160, 165, 168, 170, 173, 178, 192, 194, 218, 240, 264, 280, 285, 288, 290, 293, 298, 312, 314, 336, 338, 352, 357, 360, 365, 370, 386, 408, 410, 432, 458, 480, 482

Offset: 1

Hugo Pfoertner, Oct 22 2003

nonn

			a(1)=3*3-2*2=5, a(2)=3*3+2*2=13, a(3)=5*5-3*3=16

Cf. A001481, A062316, A088909.

A088918 Number of representations of n as sum of two squares of distinct primes.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Reinhard Zumkeller, Oct 23 2003

nonn

a(n) <= A000161(n); a(A088909(n)) > 0;

a(A088919(n)) = n and a(k) <> n for k < A088919(n).

			a(410)=2, see A088919.

Index entries for sequences related to sums of squares

Cf. A002654.

cp's OEIS Frontend

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.

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A088908 Numbers expressible as sum or difference of the squares of two distinct primes.

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A088918 Number of representations of n as sum of two squares of distinct primes.

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