

A129011


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


4



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, 73, 77, 81, 85, 89, 93, 97, 101, 105, 110, 114, 118, 123, 127, 132, 136, 141, 145, 150, 155, 160, 164, 169, 174, 179, 184, 189, 194, 199, 204, 209, 214, 219, 224, 229, 234
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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. 293308.


LINKS

Table of n, a(n) for n=0..60.
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. 248250 (1946).
L. Székely, Crossing numbers and hard Erdős problems in discrete geometry, Combin. Probab. Comput. 6(1997).


FORMULA

a(n) = floor(n^(4/3)) = A048766(A000583(n)).


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

Cf. A000583, A048766.
Sequence in context: A186289 A332687 A053044 * A130174 A061168 A130798
Adjacent sequences: A129008 A129009 A129010 * A129012 A129013 A129014


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, May 01 2007


EXTENSIONS

More terms from Robert G. Wilson v, May 02 2007


STATUS

approved



