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A002859 a(1)=1, a(2)=3; for n >= 3, a(n) is smallest number that is uniquely of the form a(j) + a(k) with 1 <= j < k < n.
(Formerly M2303 N0909)
10
1, 3, 4, 5, 6, 8, 10, 12, 17, 21, 23, 28, 32, 34, 39, 43, 48, 52, 54, 59, 63, 68, 72, 74, 79, 83, 98, 99, 101, 110, 114, 121, 125, 132, 136, 139, 143, 145, 152, 161, 165, 172, 176, 187, 192, 196, 201, 205, 212, 216, 223, 227, 232, 234, 236, 243, 247, 252, 256, 258 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

An Ulam-type sequence - see A002858 for many further references, comments, etc.

REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 145-151.

R. K. Guy, Unsolved Problems in Number Theory, Section C4.

R. K. Guy, "s-Additive sequences," preprint, 1994.

C. Pickover, Mazes for the Mind, St. Martin's Press, NY, 1992, p. 358.

R. Queneau, Sur les suites s-additives, J. Combin. Theory, A12 (1972), 31-71.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

S. M. Ulam, Problems in Modern Mathematics, Wiley, NY, 1960, p. ix.

LINKS

T. D. Noe, Table of n, a(n) for n=1..10000

S. R. Finch, Ulam s-Additive Sequences

N. J. A. Sloane, Handwritten notes on Self-Generating Sequences, 1970 (note that A1148 has now become A005282)

S. M. Ulam, On some mathematical problems connected with patterns of growth of figures, pp. 215-224 of R. E. Bellman, ed., Mathematical Problems in the Biological Sciences, Proc. Sympos. Applied Math., Vol. 14, Amer. Math. Soc., 1962 [Annotated scanned copy]

Eric Weisstein's World of Mathematics, Ulam Sequence

Wikipedia, Ulam number

Index entries for Ulam numbers

EXAMPLE

7 is missing since 7 = 1 + 6 = 3 + 4; but 8 is present since 8 = 3 + 5 has a unique representation.

MATHEMATICA

s = {1, 3}; Do[ AppendTo[s, n = Last[s]; While[n++; Length[ DeleteCases[ Intersection[s, n-s], n/2, 1, 1]] != 2]; n], {60}]; s (* Jean-Fran├žois Alcover, Oct 20 2011 *)

PROG

(Haskell)

a002859 n = a002859_list !! (n-1)

a002859_list = 1 : 3 : ulam 2 3 a002859_list

-- Function ulam as defined in A002858.

-- Reinhard Zumkeller, Nov 03 2011

CROSSREFS

Cf. A002858 (version beginning 1,2), A199118, A199119.

Sequence in context: A051916 A130216 A120162 * A180646 A062514 A065875

Adjacent sequences:  A002856 A002857 A002858 * A002860 A002861 A002862

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane, Mira Bernstein

STATUS

approved

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Last modified May 24 22:11 EDT 2017. Contains 287008 sequences.