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

%I A031980 #25 Feb 16 2025 08:32:36
%S A031980 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,
%T A031980 27,29,30,31,32,33,34,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
%U A031980 52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,73,74,75,76,77
%N A031980 a(n) is the smallest number >= 1 not occurring earlier and not the sum of cubes of two distinct earlier terms.
%D A031980 Mihaly Bencze [Beneze], Smarandache recurrence type sequences, Bulletin of pure and applied sciences, Vol. 16E, No. 2, 1997, pp. 231-236.
%D A031980 F. Smarandache, Properties of numbers, ASU Special Collections, 1973.
%H A031980 Klaus Brockhaus, <a href="/A031980/b031980.txt">Table of n, a(n) for n = 1..4900</a>
%H A031980 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/Sequences-book.pdf">Sequences of Numbers Involved in Unsolved Problems</a>.
%H A031980 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmarandacheSequences.html">Smarandache Sequences</a>
%t A031980 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 *)
%o A031980 (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
%Y A031980 Cf. A024670 (sums of cubes of two distinct positive integers), A001235 (sums of two cubes in more than one way), A141805 (complement).
%K A031980 nonn,nice,easy
%O A031980 1,2
%A A031980 J. Castillo (arp(AT)cia-g.com) [Broken email address?]
%E A031980 More terms from Larry Reeves (larryr(AT)acm.org), Sep 26 2000
%E A031980 Better definition from _Klaus Brockhaus_, Jul 16 2008