A141805 Complement of A031980.

9, 28, 35, 65, 72, 91, 126, 133, 152, 189, 217, 224, 243, 280, 341, 344, 351, 370, 407, 468, 513, 520, 539, 559, 576, 637, 728, 855, 1001, 1008, 1027, 1064, 1125, 1216, 1332, 1339, 1343, 1358, 1395, 1456, 1512, 1547, 1674, 1729, 1736, 1755, 1792, 1843, 1853

Offset

1,1

Comments

Subsequence of A024670; A141806 gives the terms of A024670 that are not in this sequence.

Not a supersequence of A001235; 7094269 is the smallest number that is in A001235 but not in this sequence (see third example below), the next number is 11261376.

Links

Klaus Brockhaus, Table of n, a(n) for n = 1..24834

Index to sequences related to sums of squares and sums of cubes

Example

9 is the sum of two distinct nonzero cubes in exactly one way: 9 = 1^3 + 2^3. 9 is not in A031980 because 1 and 2 are earlier terms of A031980. Therefore 9 is a term of this sequence.
1729 is the sum of two distinct nonzero cubes in exactly two ways: 1729 = 9^3 + 10^3 = 1^3 + 12^3. 1729 is not in A031980 because 1 and 12 are earlier terms of A031980. Therefore 1729 is a term of this sequence.
7094269 is the sum of two distinct nonzero cubes in exactly two ways: 7094269 = 70^3 + 189^3 = 133^3 + 168^3. 7094269 is in A031980 because it not the sum of cubes of two earlier terms of A031980; in the first case 189 and in the second case 133 is not a term of A031980. Therefore 7094269 is not a term of this sequence.

Mathematica

max = 2000; A031980 = {1}; Do[ m = Ceiling[(n - 1)^(1/3)]; s = Select[ A031980, # <= m &]; ls = Length[s]; sumOfCubes = Union[Flatten[ Table[s[[i]]^3 + s[[j]]^3, {i, 1, ls}, {j, i + 1, ls}]]]; If[FreeQ[sumOfCubes, n], AppendTo[ A031980, n] ], {n, 2, max}]; Complement[Range[max], A031980] (* Jean-François Alcover, Sep 03 2013 *)

Prog

(Magma) m:=1853; a:=[]; a2:={}; for n in [1..m] do p:=1; u:= a2 join { x: x in a }; while p in u do p:=p+1; end while; if p gt m then break; end if; a2:=a2 join { x^3 + p^3: x in a | x^3 + p^3 le m }; Append(~a, p); end for; print a2;

Crossrefs

Cf. A141806, A031980 (smallest number not occurring earlier and not the sum of cubes of two distinct earlier terms), A024670 (sums of cubes of two distinct positive integers), A001235 (sums of two cubes in more than one way).

Sequence in context: A334185 A267686 A024670 * A256497 A124360 A041152

Adjacent sequences: A141802 A141803 A141804 * A141806 A141807 A141808

Keyword

nonn

Author

Klaus Brockhaus, Jul 16 2008

Status

approved