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

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

Author

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

Keywords

• nonn
• nice
• easy

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

• Klaus Brockhaus, Table of n, a(n) for n = 1..4900
• F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.
• Eric Weisstein's World of Mathematics, Smarandache Sequences

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