OFFSET
0,3
COMMENTS
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
REFERENCES
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.
LINKS
R. Churchhouse, A New Theorem in the Additive Theory of Numbers
P. Erdős, On sets of distances of n points, American Mathematical Monthly 53, pp. 248-250 (1946).
L. Székely, Crossing numbers and hard Erdős problems in discrete geometry, Combin. Probab. Comput. 6(1997).
MATHEMATICA
Table[ Floor[n^(4/3)], {n, 0, 60}] (* Robert G. Wilson v, May 02 2007 *)
PROG
(PARI) a(n) = floor(n^(4/3)); \\ Altug Alkan, Dec 20 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, May 01 2007
EXTENSIONS
More terms from Robert G. Wilson v, May 02 2007
STATUS
approved