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A006844 a(1)=4, a(2)=5; thereafter a(n) is smallest number that is greater than a(n-1) 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
This is the 1-additive 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 Ulam-type sequence - see A002858 for many further references, comments, etc. - T. D. Noe, Jan 21 2008
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 145-151.
R. K. Guy, "s-Additive 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
Experimental Mathematics, Home Page
Steven R. Finch, Stolarsky-Harborth Constant [Broken link]
Steven R. Finch, Stolarsky-Harborth Constant [From the Wayback machine]
Steven R. Finch, Patterns in 1-additive sequences, Experimental Mathematics 1 (1992), 57-63.
R. K. Guy, s-Additive sequences, Preprint, 1994. (Annotated scanned copy)
R. Queneau, Sur les suites s-additives, J. Combin. Theory, A12 (1972), 31-71.
Eric Weisstein's World of Mathematics, Ulam Sequence
Wikipedia, Ulam number
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}] (* Jean-François Alcover, Apr 03 2013 *)
PROG
(Haskell)
a006844 n = a006844_list !! (n-1)
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 A331531
KEYWORD
easy,nonn,nice
AUTHOR
STATUS
approved

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Last modified February 21 08:45 EST 2024. Contains 370228 sequences. (Running on oeis4.)