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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Comments

Indices of A034404. - Harvey P. Dale, Jul 25 2011

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.

Crossrefs

Cf. A000292, A010330, A034404.

Programs

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