

A001857


a(1)=2, 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 M0634 N0231)


8



2, 3, 5, 7, 8, 9, 13, 14, 18, 19, 24, 25, 29, 30, 35, 36, 40, 41, 46, 51, 56, 63, 68, 72, 73, 78, 79, 83, 84, 89, 94, 115, 117, 126, 153, 160, 165, 169, 170, 175, 176, 181, 186, 191, 212, 214, 230, 235, 240, 245, 266, 273, 278, 283, 288, 325, 331, 332, 337, 342
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OFFSET

1,1


COMMENTS

An Ulamtype sequence  see A002858 for many further references, comments, etc.
A plot of the first 10^6 terms shows a nearly straight line having a slope of about 11.1. In contrast to A002858, this sequence has many consecutive numbers; of the first 10^6 terms, consecutive numbers appear 141674 times!  T. D. Noe, Jan 21 2008


REFERENCES

S. R. Finch, Patterns in 1additive sequences, Experimental Mathematics 1 (1992), 5763.
S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 145151.
R. K. Guy, Unsolved Problems in Number Theory, Section C4.
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



MATHEMATICA

s = {2, 3}; Do[ AppendTo[s, n = Last[s]; While[n++; Length[ DeleteCases[ Intersection[s, ns], n/2, 1, 1]] != 2]; n], {100}]; s (* JeanFrançois Alcover, Sep 08 2011 *)


PROG

(Haskell)
a001857 n = a001857_list !! (n1)
a001857_list = 2 : 3 : ulam 2 3 a001857_list
 Function ulam as defined in A002858.


CROSSREFS



KEYWORD

nonn,nice


AUTHOR



EXTENSIONS



STATUS

approved



