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

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

Offset: 0

Author

Jonathan Vos Post, May 01 2007

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A000583, A048766.

Programs

Mathematica

Table[ Floor[n^(4/3)], {n, 0, 60}] (* Robert G. Wilson v, May 02 2007 *)

PARI

a(n) = floor(n^(4/3)); \\ Altug Alkan, Dec 20 2015

PARI

a(n) = sqrtnint(n^4, 3); \\ Michel Marcus, Apr 30 2025

Formula

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

Extensions

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