A078139 Primes which cannot be written as sum of squares>1.

2, 3, 5, 7, 11, 19, 23

Offset: 1

Author

Reinhard Zumkeller, Nov 19 2002

Keywords

• nonn
• fini
• full

Comments

From Hieronymus Fischer, Nov 11 2007: (Start)

Equivalently, prime numbers which cannot be written as sum of squares of primes (see A078137 for the proof).

Equivalently, prime numbers which cannot be written as sum of squares of 2 and 3 (see A078137 for the proof).

The sequence is finite, since numbers > 23 can be written as sums of squares >1 (see A078135).

Explicit representation as sum of squares of primes, or rather of squares of 2 and 3, for numbers m>23: we have m=c*2^2+d*3^2, where c:=(floor(m/4) - 2*(m mod 4))>=0, d:=m mod 4. For that, the finiteness of the sequence is proved. (End)

Links

• Eric Weisstein's World of Mathematics, Square Number.
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000290, A078134, A078138, A000040, A078133.

Cf. A078135, A090677, A078137, A134754, A134755.