A003666 - OEIS

%I M3237 #32 Mar 13 2023 08:41:10

%S 1,4,5,6,7,8,10,16,18,19,21,31,32,33,42,46,56,57,66,70,79,82,91,96,

%T 104,105,107,116,129,130,131,141,158,165,168,179,180,182,191,204,205,

%U 206,216,217,218,219,229,230,244,256,266,267,268,281,290,315,316,317,318,328

%N a(n) is smallest number which is uniquely of the form a(j) + a(k) with 1 <= j < k < n and a(1) = 1, a(2) = 4.

%C An Ulam-type sequence - see A002858 for many further references, comments, etc. - _T. D. Noe_, Jan 21 2008

%D R. K. Guy, "s-Additive sequences", preprint, 1994.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A003666/b003666.txt">Table of n, a(n) for n = 1..10000</a>

%H S. R. Finch, <a href="http://www.emis.de/journals/EM/">Patterns in 1-additive sequences</a>, Experimental Mathematics 1 (1992), 57-63.

%H R. K. Guy, <a href="/A007300/a007300.pdf">s-Additive sequences</a>, Preprint, 1994. (Annotated scanned copy)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UlamSequence.html">Ulam Sequence</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Ulam_number">Ulam number</a>

%H <a href="/index/U#Ulam_num">Index entries for Ulam numbers</a>

%t Nest[Append[#, SelectFirst[Union@ Select[Tally@ Map[Total, Select[Permutations[#, {2}], #1 < #2 & @@ # &]], Last@ # == 1 &][[All, 1]], Function[k, FreeQ[#, k]]]] &, {1, 4}, 58] (* _Michael De Vlieger_, Nov 16 2017 *)

%o (Haskell)

%o a003666 n = a003666_list !! (n-1)

%o a003666_list = 1 : 4 : ulam 2 4 a003666_list

%o -- Function ulam as defined in A002858.

%o -- _Reinhard Zumkeller_, Nov 03 2011

%Y Cf. A003662, A199120, A199121.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, _Mira Bernstein_