A283019 -id:A283019 - cp's OEIS frontend

A283017 Primes which are the sum of three nonzero 6th powers.

3, 857, 1459, 4889, 50753, 51481, 66377, 119107, 210961, 262937, 308801, 525017, 531569, 539633, 562691, 766739, 797681, 840241, 1000793, 1046657, 1078507, 1772291, 1864873, 2303003, 2834443, 2986777, 3032641, 3107729, 3365777, 4757609, 4804201, 5135609, 5987593, 7530329, 7534361, 7743529, 8061041

Offset: 1

Ilya Gutkovskiy, Feb 26 2017

nonn

Primes of form x^6 + y^6 + z^6 where x, y, z > 0.

			3 = 1^6 + 1^6 + 1^6;
857 = 2^6 + 2^6 + 3^6;
1459 = 1^6 + 3^6 + 3^6, etc.

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

Cf. A001014, A003359, A007490, A085317, A085318, A085319, A283018, A283019.

N:= 10^8: # to get all terms <= N
S:= [seq(i^6, i=1..floor(N^(1/6)))]:
S3:= {seq(seq(seq(S[i]+S[j]+S[k],k=1..j),j=1..i),i=1..nops(S))}:
sort(convert(select(t -> t <= N and isprime(t), S3), list)); # Robert Israel, Mar 09 2017

nn = 15; Select[Union[Plus @@@ (Tuples[Range[nn], {3}]^6)], # <= nn^6 && PrimeQ[#] &]

list(lim)=my(v=List(),a6,a6b6,t); lim\=1; for(a=1,sqrtnint(lim-2,6), a6=a^6; for(b=1,min(sqrtnint(lim-a6-1,6),a), a6b6=a6+b^6; forstep(c=if(a6b6%2,2,1),min(sqrtnint(lim-a6b6,6),b),2, if(isprime(t=a6b6+c^6), listput(v,t))))); Set(v) \\ Charles R Greathouse IV, Mar 09 2017

A283018 Primes which are the sum of three positive 7th powers.

Original entry on oeis.org

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

Offset: 1

Ilya Gutkovskiy, Feb 26 2017

nonn

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

			3 = 1^7 + 1^7 + 1^7;
257 = 1^7 + 2^7 + 2^7;
82499 = 3^7 + 3^7 + 5^7, etc.

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

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

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

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

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

cp's OEIS Frontend

A283017 Primes which are the sum of three nonzero 6th powers.

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