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A020894 Nonnegative numbers that are sums of two nonzero cubes. 2
0, 2, 7, 9, 16, 19, 26, 28, 35, 37, 54, 56, 61, 63, 65, 72, 91, 98, 117, 124, 126, 127, 128, 133, 152, 169, 189, 208, 215, 217, 218, 224, 243, 250, 271, 279, 280, 296, 316, 331, 335, 341, 342, 344, 351, 370, 386, 387, 397, 407, 432, 448, 468, 469 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
From Michael B. Porter, Oct 16 2009: (Start)
When calculating terms, there is no need to search beyond a value x defined by x^3 - (x-1)^3 = n. The positive solution is given by x = 1/2 + (sqrt(12n-3))/6.
There are no cubes in this sequence, but the numbers before and after a cube are all included. (End)
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Steven R. Finch, On a Generalized Fermat-Wiles Equation [broken link]
Steven R. Finch, On a Generalized Fermat-Wiles Equation [From the Wayback Machine]
EXAMPLE
From Michael B. Porter, Oct 16 2009: (Start)
7 is in the sequence because 2^3 + (-1)^3 = 7
8 is not in the sequence because the only solutions to x^3 + y^3 = 8 have either x=0 or y=0. (End)
MATHEMATICA
Reap[For[n = 0, n < 500, n++, fi = FindInstance[x > 0 && y != 0 && n == x^3 + y^3, {x, y}, Integers, 1]; If[fi =!= {}, Print[n, " = ", Hold[x^3 + y^3] /. fi[[1]]]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Nov 05 2016 *)
PROG
(PARI) isA020894(n) = {r=0; x=1.0/2+sqrt(12*n-3.0)/6; for(i=1, floor(x), if(ispower(n-i^3, 3) & (n != i^3), r++)); r>0}; \\ Michael B. Porter, Oct 16 2009
(PARI) T=thueinit('z^3+1);
is(n)=n==0 || #select(v->v[1] && v[2], thue(T, n))>0 \\ Charles R Greathouse IV, Nov 29 2014
CROSSREFS
Cf. A045980 [From Michael B. Porter, Oct 16 2009]
Sequence in context: A098017 A225675 A185869 * A165995 A287575 A267212
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition and offset edited by N. J. A. Sloane, Dec 01 2009
STATUS
approved

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Last modified May 30 06:59 EDT 2024. Contains 372962 sequences. (Running on oeis4.)