OFFSET
1,1
COMMENTS
If two primes which end in 3 or 7 and surpass by 3 a multiple of 4 are multiplied, then their product will be composed of a square and the quintuple of another square. (Fermat (1654))
REFERENCES
Dedekind R., Theory of Algebraic Integers, Cambridge Univ. Press, 1996 (translation of the 1877 French original), pp. 12-13.
LINKS
Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000
EXAMPLE
94 = 7^2 + 5*3^2, therefore 94 is a term.
MATHEMATICA
n = 889; limx = Sqrt[n]; limy = Sqrt[n/5]; Select[Union@Flatten@Table[x^2 + 5*y^2, {x, limx}, {y, limy}], # <= n && PrimeOmega[#] == 2 &]
Select[Select[Range[889], PrimeOmega[#] == 2 &], Length@FindInstance[y > 0 && x^2 + 5*y^2 == #, {x, y}, Integers] > 0 &] (* Arkadiusz Wesolowski, Jan 13 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Arkadiusz Wesolowski, Nov 04 2012
STATUS
approved