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 A003668 a(n) is smallest number which is uniquely a(j)+a(k), j
 2, 7, 9, 11, 13, 15, 16, 17, 19, 21, 25, 29, 33, 37, 39, 45, 47, 53, 61, 69, 71, 73, 75, 85, 89, 101, 103, 117, 133, 135, 137, 139, 141, 143, 145, 147, 151, 155, 159, 163, 165, 171, 173, 179, 187, 195, 197, 199, 201, 211, 215, 227, 229, 243, 259, 261, 263, 265, 267, 269 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS An Ulam-type sequence - see A002858 for many further references, comments, etc. - T. D. Noe, Jan 21 2008 REFERENCES R. K. Guy, "s-Additive sequences", preprint, 1994. 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 M. Akeran, On some 1-additive sequences J. Cassaigne and S. R. Finch, A class of 1-additive sequences and additive recurrences S. R. Finch, Patterns in 1-additive sequences, Experimental Mathematics 1 (1992), 57-63. R. K. Guy, s-Additive sequences, Preprint, 1994. (Annotated scanned copy) Eric Weisstein's World of Mathematics, Ulam Sequence Wikipedia, Ulam number Index entries for Ulam numbers FORMULA Akeran gives a formula. For n>7, a(n+26)=a(n)+126. - T. D. Noe, Jan 21 2008 MATHEMATICA Nest[Append[#, SelectFirst[Union@ Select[Tally@ Map[Total, Select[Permutations[#, {2}], #1 < #2 & @@ # &]], Last@ # == 1 &][[All, 1]], Function[k, FreeQ[#, k]]]] &, {2, 7}, 58] (* Michael De Vlieger, Nov 16 2017 *) PROG (Haskell) a003668 n = a003668_list !! (n-1) a003668_list = 2 : 7 : ulam 2 7 a003668_list -- Function ulam as defined in A002858. -- Reinhard Zumkeller, Nov 03 2011 (Python) def aupton(terms): alst = [2, 7] for n in range(2, terms): sums = [alst[j]+alst[k] for j in range(n-1) for k in range(j+1, n)] alst.append(min([s for s in sums if sums.count(s)==1 and s > alst[-1]])) return alst print(aupton(60)) # Michael S. Branicky, Feb 07 2021 CROSSREFS Cf. A100729. Sequence in context: A047526 A221280 A166570 * A191263 A287359 A022424 Adjacent sequences: A003665 A003666 A003667 * A003669 A003670 A003671 KEYWORD nonn AUTHOR N. J. A. Sloane, Mira Bernstein STATUS approved

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Last modified September 11 17:54 EDT 2024. Contains 375839 sequences. (Running on oeis4.)