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A002311 Numbers k such that the k-th tetrahedral number is the sum of 2 tetrahedral numbers.

%I A002311 M3498 N1419 #45 Dec 27 2023 13:19:27
%S A002311 4,15,55,58,74,109,110,119,140,175,245,294,418,435,452,474,492,528,
%T A002311 535,550,562,588,644,688,702,714,740,747,753,818,868,908,918,1098,
%U A002311 1158,1220,1241,1428,1434,1444,1450,1645,1708,1738,1786,1868,2170,2183,2220,2256
%N A002311 Numbers k such that the k-th tetrahedral number is the sum of 2 tetrahedral numbers.
%C A002311 Indices of A034404. - _Harvey P. Dale_, Jul 25 2011
%D A002311 Aviezri S. Fraenkel, Diophantine equations involving generalized triangular and tetrahedral numbers, pp. 99-114 of A. O. L. Atkin and B. J. Birch, editors, Computers in Number Theory. Academic Press, NY, 1971.
%D A002311 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002311 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002311 T. D. Noe, <a href="/A002311/b002311.txt">Table of n, a(n) for n = 1..463</a>
%H A002311 H. Finner and K. Strassburger, <a href="http://dx.doi.org/10.1007/s001840100117">Increasing sample sizes do not necessarily increase the power of UMPU-tests for 2 X 2-tables</a>, Metrika, 54, 77-91, (2001).
%H A002311 M. Wunderlich, <a href="http://dx.doi.org/10.1090/S0025-5718-1962-0148608-X">Certain properties of pyramidal and figurate numbers</a>, Math. Comp., 16 (1962), 482-486.
%F A002311 a(n) = A010330(n) - 2. - _Reinhard Zumkeller_, May 02 2014
%t A002311 With[{tetras=Binomial[Range[1100]+2,3]},Flatten[Position[tetras,#]&/@ Union[Select[Total/@Tuples[tetras,2],MemberQ[tetras,#]&]]]] (* _Harvey P. Dale_, Jul 26 2011 *)
%o A002311 (Haskell)
%o A002311 import Data.List (intersect)
%o A002311 a002311 n = a002311_list !! (n-1)
%o A002311 a002311_list = filter f [1..] where
%o A002311    f x = not $ null $ intersect txs $ map (tx -) $ txs where
%o A002311        txs = takeWhile (< tx) a000292_list; tx = a000292 x
%o A002311 -- _Reinhard Zumkeller_, May 02 2014
%Y A002311 Cf. A000292, A010330, A034404.
%K A002311 nonn,easy,nice
%O A002311 1,1
%A A002311 _N. J. A. Sloane_