A002311 Numbers k such that the k-th tetrahedral number is the sum of 2 tetrahedral numbers.
4, 15, 55, 58, 74, 109, 110, 119, 140, 175, 245, 294, 418, 435, 452, 474, 492, 528, 535, 550, 562, 588, 644, 688, 702, 714, 740, 747, 753, 818, 868, 908, 918, 1098, 1158, 1220, 1241, 1428, 1434, 1444, 1450, 1645, 1708, 1738, 1786, 1868, 2170, 2183, 2220, 2256
Offset: 1
References
- 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.
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- T. D. Noe, Table of n, a(n) for n = 1..463
- H. Finner and K. Strassburger, Increasing sample sizes do not necessarily increase the power of UMPU-tests for 2 X 2-tables, Metrika, 54, 77-91, (2001).
- M. Wunderlich, Certain properties of pyramidal and figurate numbers, Math. Comp., 16 (1962), 482-486.
Programs
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Haskell
import Data.List (intersect) a002311 n = a002311_list !! (n-1) a002311_list = filter f [1..] where f x = not $ null $ intersect txs $ map (tx -) $ txs where txs = takeWhile (< tx) a000292_list; tx = a000292 x -- Reinhard Zumkeller, May 02 2014 -
Mathematica
With[{tetras=Binomial[Range[1100]+2,3]},Flatten[Position[tetras,#]&/@ Union[Select[Total/@Tuples[tetras,2],MemberQ[tetras,#]&]]]] (* Harvey P. Dale, Jul 26 2011 *)
Formula
a(n) = A010330(n) - 2. - Reinhard Zumkeller, May 02 2014
Comments