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A133750 Primes which are the sum of five positive 4th powers. 0
5, 659, 709, 739, 929, 1283, 1409, 1493, 1523, 1877, 1907, 2099, 2179, 2339, 2689, 2803, 3109, 3187, 3299, 3539, 3733, 3923, 4339, 4357, 5009, 5059, 5443, 5683, 5939, 5987, 6053, 6133, 6529, 7219, 7349, 7459, 7699, 7829, 8419, 8609, 8819, 8849, 9043, 9539 (list; graph; refs; listen; history; text; internal format)
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
{primes} INTERSECTION {a^4 + b^4 + c^4 + d^4 + e^4} = A000040 INTERSECTION {A000583(a) + A000583(b) + A000583(c) + A000583(d) + A000583(e) for a,b,c,d,e > 0}
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
Sequence in context: A117709 A185820 A332165 * A203925 A198597 A180315
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Dec 31 2007
EXTENSIONS
Data corrected by Giovanni Resta, Jun 20 2016
STATUS
approved

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Last modified June 22 01:41 EDT 2024. Contains 373561 sequences. (Running on oeis4.)