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

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

Offset

1,1

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

Table of n, a(n) for n=1..7.

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.

Sequence in context: A291660 A069749 A081889 * A347337 A210186 A120628

Adjacent sequences: A078136 A078137 A078138 * A078140 A078141 A078142

Keyword

nonn,fini,full

Author

Reinhard Zumkeller, Nov 19 2002

Status

approved