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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

%I A006844 M3245 #39 Feb 16 2025 08:32:31
%S A006844 4,5,9,13,14,17,19,21,24,25,27,35,37,43,45,47,57,67,69,73,77,83,93,
%T A006844 101,105,109,113,115,123,125,133,149,153,163,173,197,201,205,209,211,
%U A006844 213,217,219,227,229,235,237,239
%N 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.
%C A006844 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
%C A006844 An Ulam-type sequence - see A002858 for many further references, comments, etc. - _T. D. Noe_, Jan 21 2008
%D A006844 Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 145-151.
%D A006844 R. K. Guy, "s-Additive sequences," preprint, 1994.
%D A006844 R. K. Guy, Unsolved Problems in Number Theory, Section C4.
%D A006844 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006844 T. D. Noe, <a href="/A006844/b006844.txt">Table of n, a(n) for n=1..1000</a>
%H A006844 Experimental Mathematics, <a href="http://www.emis.de/journals/EM/">Home Page</a>
%H A006844 Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/stlrsky/stlrsky.html">Stolarsky-Harborth Constant</a> [Broken link]
%H A006844 Steven R. Finch, <a href="http://web.archive.org/web/20010207195349/http://www.mathsoft.com/asolve/constant/stlrsky/stlrsky.html">Stolarsky-Harborth Constant</a> [From the Wayback machine]
%H A006844 Steven R. Finch, <a href="http://www.emis.de/journals/EM/expmath/volumes/1/1.html">Patterns in 1-additive sequences</a>, Experimental Mathematics 1 (1992), 57-63.
%H A006844 R. K. Guy, <a href="/A007300/a007300.pdf">s-Additive sequences</a>, Preprint, 1994. (Annotated scanned copy)
%H A006844 R. Queneau, <a href="http://dx.doi.org/10.1016/0097-3165(72)90083-0">Sur les suites s-additives</a>, J. Combin. Theory, A12 (1972), 31-71.
%H A006844 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UlamSequence.html">Ulam Sequence</a>
%H A006844 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ulam_number">Ulam number</a>
%H A006844 <a href="/index/U#Ulam_num">Index entries for Ulam numbers</a>
%F A006844 For n>9, a(n+32) = a(n) + 192. - _T. D. Noe_, Jan 21 2008
%t A006844 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 *)
%o A006844 (Haskell)
%o A006844 a006844 n = a006844_list !! (n-1)
%o A006844 a006844_list = 4 : 5 : ulam 2 5 a006844_list
%o A006844 -- Function ulam as defined in A002858.
%o A006844 -- _Reinhard Zumkeller_, Nov 03 2011
%K A006844 easy,nonn,nice
%O A006844 1,1
%A A006844 _N. J. A. Sloane_