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A078139 Primes which cannot be written as sum of squares>1. 8
2, 3, 5, 7, 11, 19, 23 (list; graph; refs; listen; history; internal format)
OFFSET

1,1

COMMENTS

Equivalently, prime numbers which cannot be written as sum of squares of primes (see A078137 for the proof). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Nov 11 2007

Equivalently, prime numbers which cannot be written as sum of squares of 2 and 3 (see A078137 for the proof). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Nov 11 2007

The sequence is finite, since numbers > 23 can be written as sums of squares >1 (see A078135). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Nov 11 2007

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. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Nov 11 2007

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.

Sequence in context: A018146 A069749 A081889 * A120628 A143260 A039986

Adjacent sequences:  A078136 A078137 A078138 * A078140 A078141 A078142

KEYWORD

nonn,fini,full

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 19 2002

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Last modified February 15 05:38 EST 2012. Contains 205694 sequences.