

A006844


a(1)=4, a(2)=5; thereafter a(n) is smallest number that is greater than a(n1) and having a unique representation as a(j) + a(k) for j<k.
(Formerly M3245)


3



4, 5, 9, 13, 14, 17, 19, 21, 24, 25, 27, 35, 37, 43, 45, 47, 57, 67, 69, 73, 77, 83, 93, 101, 105, 109, 113, 115, 123, 125, 133, 149, 153, 163, 173, 197, 201, 205, 209, 211, 213, 217, 219, 227, 229, 235, 237, 239
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OFFSET

1,1


COMMENTS

This is the 1additive sequence with base {4,5}. Apart from three extra terms (4, 14, 24) in the initial segment, this breaks up naturally into segments of 32 terms each. [Finch, 1992].  N. J. A. Sloane, Aug 12 2015
An Ulamtype sequence  see A002858 for many further references, comments, etc.  T. D. Noe, Jan 21 2008


REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 145151.
R. K. Guy, "sAdditive sequences," preprint, 1994.
R. K. Guy, Unsolved Problems in Number Theory, Section C4.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS



FORMULA

For n>9, a(n+32) = a(n) + 192.  T. D. Noe, Jan 21 2008


MATHEMATICA

s = {4, 5}; n0 = 9; dn = 32; m = 192; Do[ AppendTo[s, n = Last[s]; While[n++; Length[ DeleteCases[ Intersection[s, n  s], n/2, 1, 1]] != 2]; n], {n0 + dn}]; Clear[a]; a[n_] := a[n] = If[n <= n0 + dn, s[[n]], a[n  dn] + m]; Table[a[n], {n, 1, 200}] (* JeanFrançois Alcover, Apr 03 2013 *)


PROG

(Haskell)
a006844 n = a006844_list !! (n1)
a006844_list = 4 : 5 : ulam 2 5 a006844_list
 Function ulam as defined in A002858.


CROSSREFS



KEYWORD

easy,nonn,nice


AUTHOR



STATUS

approved



