0,3

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]

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.

T. D. Noe, Table of n, a(n) for n=0..300

(PARI) a(n)=if(n<=1, n==1, 2*a(n-1)-a(n-1-(sqrtint(8*n-15)+1)\2))

Cf. A037254, A096858, A096796, A096824.

Adjacent sequences: A005315 A005316 A005317 this_sequence A005319 A005320 A005321

Sequence in context: A006744 A054175 A000073 this_sequence A102111 A059633 A088353

nonn,easy,nice

njas

More terms from Larry Reeves (larryr(AT)acm.org), Sep 21 2000