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A003666 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.
(Formerly M3237)
7
1, 4, 5, 6, 7, 8, 10, 16, 18, 19, 21, 31, 32, 33, 42, 46, 56, 57, 66, 70, 79, 82, 91, 96, 104, 105, 107, 116, 129, 130, 131, 141, 158, 165, 168, 179, 180, 182, 191, 204, 205, 206, 216, 217, 218, 219, 229, 230, 244, 256, 266, 267, 268, 281, 290, 315, 316, 317, 318, 328 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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
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
MATHEMATICA
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 *)
PROG
(Haskell)
a003666 n = a003666_list !! (n-1)
a003666_list = 1 : 4 : ulam 2 4 a003666_list
-- Function ulam as defined in A002858.
-- Reinhard Zumkeller, Nov 03 2011
CROSSREFS
Sequence in context: A078778 A037356 A139199 * A334917 A295742 A047314
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)