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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

T. D. Noe, Table of n, a(n) for n=1..1000

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

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}] (* Jean-Fran├žois 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 A328223

Adjacent sequences:  A006841 A006842 A006843 * A006845 A006846 A006847

KEYWORD

easy,nonn,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 21 06:00 EST 2019. Contains 329350 sequences. (Running on oeis4.)