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A283018 Primes which are the sum of three positive 7th powers. 3
3, 257, 82499, 823799, 1119863, 2099467, 4782971, 5063033, 5608699, 6880249, 7160057, 10018571, 10078253, 10094509, 10279937, 10389481, 10823671, 19503683, 20002187, 20388839, 24782969, 31584323, 35850379, 36189869, 37931147, 50614777, 57416131, 62765029, 64845797, 68355029, 71663617, 73028453 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes of form x^7 + y^7 + z^7 where x, y, z > 0.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

3 = 1^7 + 1^7 + 1^7;

257 = 1^7 + 2^7 + 2^7;

82499 = 3^7 + 3^7 + 5^7, etc.

MAPLE

N:= 10^9: # to get all terms <= N

Res:= {}:

for x from 1 to floor(N^(1/7)) do

  for y from 1 to min(x, floor((N-x^7)^(1/7))) do

    for z from 1 to min(y, floor((N-x^7-y^7)^(1/7))) do

      p:= x^7 + y^7 + z^7;

      if isprime(p) then Res:= Res union {p} fi

od od od:

sort(convert(Res, list)); # Robert Israel, Feb 26 2017

MATHEMATICA

nn = 14; Select[Union[Plus @@@ (Tuples[Range[nn], {3}]^7)], # <= nn^7 && PrimeQ[#] &]

PROG

(PARI) list(lim)=my(v=List(), x7, y7, t, p); for(x=1, sqrtnint(lim\3, 7), x7=x^7; for(y=x, sqrtnint((lim-x7)\2, 7), y7=y^7; t=x7+y7; forstep(z=y+(x+1)%2, sqrtnint((lim-t)\1, 7), 2, if(isprime(p=t+z^7), listput(v, p))))); Set(v) \\ Charles R Greathouse IV, Feb 27 2017

CROSSREFS

Cf. A001015, A003370, A007490, A085317, A085318, A085319, A283017, A283019.

Sequence in context: A051490 A232545 A177748 * A003381 A219550 A319587

Adjacent sequences:  A283015 A283016 A283017 * A283019 A283020 A283021

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 26 2017

STATUS

approved

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Last modified July 23 12:19 EDT 2021. Contains 346259 sequences. (Running on oeis4.)