

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

T. D. Noe, Table of n, a(n) for n=1..1000
Experimental Mathematics, Home Page
Steven R. Finch, StolarskyHarborth Constant [Broken link]
Steven R. Finch, StolarskyHarborth Constant [From the Wayback machine]
Steven R. Finch, Patterns in 1additive sequences, Experimental Mathematics 1 (1992), 5763.
R. K. Guy, sAdditive sequences, Preprint, 1994. (Annotated scanned copy)
R. Queneau, Sur les suites sadditives, J. Combin. Theory, A12 (1972), 3171.
Eric Weisstein's World of Mathematics, Ulam Sequence
Wikipedia, Ulam number
Index entries for Ulam numbers


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.
 Reinhard Zumkeller, Nov 03 2011


CROSSREFS

Sequence in context: A229240 A322135 A034705 * A022425 A277549 A328223
Adjacent sequences: A006841 A006842 A006843 * A006845 A006846 A006847


KEYWORD

easy,nonn,nice


AUTHOR

N. J. A. Sloane


STATUS

approved



