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Search: id:A005318
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| A005318 |
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Conway-Guy sequence: a(n + 1) = 2a(n) - a(n - floor( 1/2 + sqrt(2n) )).
(Formerly M1075)
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+0
7
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| 0, 1, 2, 4, 7, 13, 24, 44, 84, 161, 309, 594, 1164, 2284, 4484, 8807, 17305, 34301, 68008, 134852, 267420, 530356, 1051905, 2095003, 4172701, 8311101, 16554194, 32973536, 65679652, 130828948, 261127540, 521203175, 1040311347, 2076449993
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Conway and Guy conjecture that the set of k numbers {s_i = a(k) - a(k-i) : 1 <= i <= k} has the property that all its subsets have distinct sums - see Guy's book. These k-sets are the rows of A096858. [This conjecture has apparently now been proved by Bohman. - I. Halupczok (integerSequences(AT)karimmi.de), Feb 20 2006]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Tom Bohman: A sum packing problem of Erdos and the Conway-Guy sequence. Proc. AMS 124, (No. 12, 1996), pp. 3627-3636.
P. Borwein and M. J. Mossinghoff, Newman Polynomials with Prescribed Vanishing and Integer Sets with Distinct Subset Sums, Math. Comp., 72 (2003), 787-800.
J. H. Conway and R. K. Guy, Solution of a problem of Erdos, Colloq. Math. 20 (1969), p. 307.
R. K. Guy, Sets of integers whose subsets have distinct sums, pp. 141-154 of Theory and practice of combinatorics. Ed. A. Rosa, G. Sabidussi and J. Turgeon. Annals of Discrete Mathematics, 12. North-Holland 1982.
R. K. Guy, Unsolved Problems in Number Theory, C8.
Kreweras, G.; Sur quelques problemes relatifs au vote pondere [Some problems of weighted voting], Math. Sci. Humaines No. 84 (1983), 45-63.
G. Kreweras, Alvarez Rodriguez, Miguel-Angel; Ponderation entiere minimale de N telle que pour tout k toutes les k-parties de N aient des poids distincts. [Minimal integer weighting of N such that for any k all the k-subsets of N have unequal weights] C. R. Acad. Sci. Paris Ser. I Math. 296 (1983), no. 8, 345-347.
M. Wald, Problem 1192, Unequal sums, J. Rec. Math., 15 (No. 2, 1983-1984), pp. 148-149.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..300
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PROGRAM
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(PARI) a(n)=if(n<=1, n==1, 2*a(n-1)-a(n-1-(sqrtint(8*n-15)+1)\2))
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CROSSREFS
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Cf. A037254, A096858, A096796, A096824.
Sequence in context: A054175 A000073 A160254 this_sequence A102111 A059633 A088353
Adjacent sequences: A005315 A005316 A005317 this_sequence A005319 A005320 A005321
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Sep 21 2000
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