| Displaying 1-2 of 2 results found.
page
1
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
EXAMPLE
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.
CROSSREFS
Cf. A024670, A141805, A031980 (smallest number not occurring earlier and not the sum of cubes of two distinct earlier terms).
a(n) is the smallest number >= 1 not occurring earlier and not the sum of cubes of two distinct earlier terms.
+10
6
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
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.
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 *)
PROG
(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
CROSSREFS
Cf. A024670 (sums of cubes of two distinct positive integers), A001235 (sums of two cubes in more than one way), A141805 (complement).
AUTHOR
J. Castillo (arp(AT)cia-g.com) [Broken email address?]
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Sep 26 2000
Search completed in 0.007 seconds
|