

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
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OFFSET

1,2


COMMENTS

An Ulamtype sequence  see A002858 for many further references, comments, etc.


REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 145151.
R. K. Guy, Unsolved Problems in Number Theory, Section C4.
R. K. Guy, "sAdditive sequences," preprint, 1994.
C. Pickover, Mazes for the Mind, St. Martin's Press, NY, 1992, p. 358.
R. Queneau, Sur les suites sadditives, J. Combin. Theory, A12 (1972), 3171.
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 sAdditive Sequences
N. J. A. Sloane, Handwritten notes on SelfGenerating Sequences, 1970 (note that A1148 has now become A005282)
S. M. Ulam, On some mathematical problems connected with patterns of growth of figures, pp. 215224 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, ns], n/2, 1, 1]] != 2]; n], {60}]; s (* JeanFrançois Alcover, Oct 20 2011 *)


PROG

(Haskell)
a002859 n = a002859_list !! (n1)
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



