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A129011
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a(n) = floor(n^(4/3)).
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4
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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
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0,3
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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FORMULA
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MATHEMATICA
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PROG
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(PARI) a(n) = floor(n^(4/3)); \\ Altug Alkan, Dec 20 2015
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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