OFFSET
1,3
COMMENTS
Since 4 is even, either x or y or both may be negative integers, because their fourth powers will then be positive.
The only prime term in this sequence is 5; this can be proved using Sophie Germain's identity.
REFERENCES
Titu Andreescu and Rǎzvan Gelca, Mathematical Olympiad Challenges, New York, Birkhäuser (2009), p. 48.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Graeme Taylor, Identity of Sophie Germain, April 1, 2006.
FORMULA
x^4 + 4y^4 = (x^2 - 2xy + 2y^2)(x^2 + 2xy + 2y^2). This is Sophie Germain's identity.
EXAMPLE
80 = 2^4 + 4 * 2^4.
81 = 3^4 + 4 * 0^4.
85 = 3^4 + 4 * 1^4.
MATHEMATICA
nn = 10; Union[Select[Flatten[Table[x^4 + 4*y^4, {x, 0, nn}, {y, 0, nn}]], # <= nn^4 &]] (* T. D. Noe, Nov 08 2013 *)
PROG
(PARI) list(lim)=my(v=List(), t); for(y=0, sqrtnint(lim\4, 4), for(x=0, sqrtnint(lim\1-(t=4*y^4), 4), listput(v, t+x^4))); Set(v) \\ Charles R Greathouse IV, Nov 07 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alonso del Arte, Oct 31 2013
STATUS
approved