cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A141806 Terms of A024670 that are not in A141805.

Original entry on oeis.org

730, 737, 756, 793, 854, 945, 1072, 1241, 2060, 2457, 2926, 3473, 4825, 5642, 6561, 7588, 8729, 9990, 11377, 12896, 14553, 16354, 18305, 20412, 21953, 21960, 21979, 22016, 22077, 22168, 22295, 22464, 22681, 22952, 23283, 23680, 24149, 24696
Offset: 1

Views

Author

Klaus Brockhaus, Jul 16 2008

Keywords

Comments

A024670 gives the sums of cubes of two distinct positive integers. A141805, the complement of A031980, is a subsequence of A024670.

Examples

			1072 is the sum of two distinct nonzero cubes in exactly one way: 1072 = 7^3 + 9^3. 9 is not in A031980, so 1072 is not the sum of cubes of two distinct earlier terms of A031980 and hence 1072 is in A031980. Therefore 1072 is in not in A141805 and so 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. 1 and 12 are in A031980, so 1729 is the sum of cubes of two distinct earlier terms of A031980 and hence 1729 is in not A031980. Therefore 1729 is in A141805 and so not a term of this sequence.

Links

Crossrefs

Cf. A024670, A141805, A031980 (smallest number not occurring earlier and not the sum of cubes of two distinct earlier terms).

A031980 a(n) is the smallest number >= 1 not occurring earlier and not the sum of cubes of two distinct earlier terms.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77
Offset: 1

Views

Author

J. Castillo (arp(AT)cia-g.com) [Broken email address?]

Keywords

References

  • Mihaly Bencze [Beneze], Smarandache recurrence type sequences, Bulletin of pure and applied sciences, Vol. 16E, No. 2, 1997, pp. 231-236.
  • F. Smarandache, Properties of numbers, ASU Special Collections, 1973.

Links

Crossrefs

Cf. A024670 (sums of cubes of two distinct positive integers), A001235 (sums of two cubes in more than one way), A141805 (complement).

Programs

  • Magma
    m:=77; 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 a; // Klaus Brockhaus, Jul 16 2008
  • Mathematica
    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, 77}]; A031980 (* Jean-François Alcover, Dec 14 2011 *)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Sep 26 2000
Better definition from Klaus Brockhaus, Jul 16 2008
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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