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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; text; 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, 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, Nov 11 2007
The sequence is finite, since numbers > 23 can be written as sums of squares >1 (see A078135). - Hieronymus Fischer, 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, Nov 11 2007
LINKS
Eric Weisstein's World of Mathematics, Square Number.
CROSSREFS
Sequence in context: A291660 A069749 A081889 * A347337 A210186 A120628
KEYWORD
nonn,fini,full
AUTHOR
Reinhard Zumkeller, Nov 19 2002
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)