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A138854
Numbers which are the sum of three cubes of distinct primes.
6
160, 378, 476, 495, 1366, 1464, 1483, 1682, 1701, 1799, 2232, 2330, 2349, 2548, 2567, 2665, 3536, 3555, 3653, 3871, 4948, 5046, 5065, 5264, 5283, 5381, 6252, 6271, 6369, 6587, 6894, 6992, 7011, 7118, 7137, 7210, 7229, 7235, 7327, 7453, 8198, 8217, 8315
OFFSET
1,1
COMMENTS
This is a subsequence of A024975. The odd terms of this sequence are A138853, the even terms are 8+{ even terms of A120398 }. Thus primes in this sequence, A137365, are the same as primes in A138853.
LINKS
FORMULA
A138854 = { p(i)^3+p(j)^3+p(k)^3 ; i>j>k>0 } = A138853 union { p(i)^3+p(j)^3+8 ; i>j>1}
MAPLE
isA030078 := proc(n)
local f ;
if n < 8 then
false;
else
f := ifactors(n)[2] ;
if nops(f) = 1 and op(2, op(1, f)) = 3 then
true;
else
false;
end if;
end if;
end proc:
isA138854 := proc(n)
local i, j, p, q, r, rcub ;
for i from 1 do
p := ithprime(i) ;
if p^3+(p+1)^3+(p+2)^3 > n then
return false;
end if;
for j from i+1 do
q := ithprime(j) ;
rcub := n-q^3-p^3 ;
if rcub <= q^3 then
break;
fi ;
if isA030078(rcub) then
return true;
end if;
end do:
end do:
end proc:
for n from 5 do
if isA138854(n) then
print(n);
end if;
end do: # R. J. Mathar, Jun 09 2014
MATHEMATICA
f[upto_]:=Module[{maxp=PrimePi[Floor[Power[upto, (3)^-1]]]}, Select[Union[Total/@(Subsets[Prime[Range[maxp]], {3}]^3)], #<=upto&]]; f[9000] (* Harvey P. Dale, Mar 21 2011 *)
PROG
(PARI) isA138854(n)={ if( n%2, isA138853(n), isA120398(n-8)) }
for( n=1, 10^4, isA138854(n) & print1(n", "))
CROSSREFS
Cf. A024975 (a^3+b^3+c^3, a>b>c>0), A138853 (odd terms of this), A120398, A137365 (primes in A138853 / A138854).
Sequence in context: A290463 A367206 A127338 * A133530 A278129 A184070
KEYWORD
nonn
AUTHOR
M. F. Hasler, Apr 13 2008
STATUS
approved