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A129011 a(n) = floor(n^(4/3)).

%I A129011 #21 Apr 30 2025 09:16:12
%S A129011 0,1,2,4,6,8,10,13,16,18,21,24,27,30,33,36,40,43,47,50,54,57,61,65,69,
%T A129011 73,77,81,85,89,93,97,101,105,110,114,118,123,127,132,136,141,145,150,
%U A129011 155,160,164,169,174,179,184,189,194,199,204,209,214,219,224,229,234
%N A129011 a(n) = floor(n^(4/3)).
%C A129011 Churchhouse (1971), as an early example of the use of computers in number theory, conjectured that every positive integer N is the sum of two elements of this sequence and verified the conjecture up to N = 10,000 using the Atlas 1 computer of the Atlas Computer Laboratory at Chilton, U.K. He was able to prove that every sufficiently large integer, N, can be expressed in the form N = floor(n^s) + floor(m^s), n and m being positive integers and s being any number in the interval (1, 4/3). - _Peter Bala_, Jan 13 2013
%D A129011 J. Spencer, E. Szemeredi and W. T. Trotter, Unit distances in the Euclidean plane, Graph Theory and Combinatorics, B. Bollabas editor, London: Academic Press, 1984, pp. 293-308.
%H A129011 R. Churchhouse, <a href="http://www.chilton-computing.org.uk/acl/applications/number/p008.htm">A New Theorem in the Additive Theory of Numbers</a>
%H A129011 P. Erdős, <a href="http://www.renyi.hu/~p_erdos/1946-03.pdf">On sets of distances of n points</a>, American Mathematical Monthly 53, pp. 248-250 (1946).
%H A129011 L. Székely, <a href="https://doi.org/10.1017/S0963548397002976">Crossing numbers and hard Erdős problems in discrete geometry</a>, Combin. Probab. Comput. 6(1997).
%F A129011 a(n) = floor(n^(4/3)) = A048766(A000583(n)).
%t A129011 Table[ Floor[n^(4/3)], {n, 0, 60}] (* _Robert G. Wilson v_, May 02 2007 *)
%o A129011 (PARI) a(n) = floor(n^(4/3)); \\ _Altug Alkan_, Dec 20 2015
%o A129011 (PARI) a(n) = sqrtnint(n^4, 3); \\ _Michel Marcus_, Apr 30 2025
%Y A129011 Cf. A000583, A048766.
%K A129011 easy,nonn
%O A129011 0,3
%A A129011 _Jonathan Vos Post_, May 01 2007
%E A129011 More terms from _Robert G. Wilson v_, May 02 2007