OFFSET
1,1
COMMENTS
Every positive integer is expressible as a sum of (at most) g(4) = 19 biquadratic numbers (Waring's problem). Davenport (1939) showed that G(4) = 16, meaning that all sufficiently large integers require only 16 biquadratic numbers.
LINKS
Eric Weisstein's World of Mathematics, Biquadratic Number.
FORMULA
EXAMPLE
a(1) = 5 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 = 1 + 1 + 1 + 1 + 1.
a(2) = 659 = 5^4 + 2^4 + 2^4 + 1^4 + 1^4 = 625 + 16 + 16 + 1 + 1.
a(3) = 709 = 5^4 + 3^4 + 1^4 + 1^4 + 1^4 = 625 + 81 + 1 + 1 + 1.
MATHEMATICA
t = Range[9]^4; Select[Union[Plus @@@ Tuples[t, 5]], # < 10^4 && PrimeQ[#] &] (* Giovanni Resta, Jun 20 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Dec 31 2007
EXTENSIONS
Data corrected by Giovanni Resta, Jun 20 2016
STATUS
approved