A003667 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) = 5.
1, 5, 6, 7, 8, 9, 10, 12, 20, 22, 23, 24, 26, 38, 39, 40, 41, 52, 57, 69, 70, 71, 82, 87, 98, 102, 113, 119, 129, 130, 133, 144, 160, 161, 162, 163, 175, 196, 205, 208, 209, 222, 223, 224, 226, 237, 253, 254, 255, 256, 268, 269, 270, 271, 272, 284, 285, 286, 303, 318
Offset: 1
Keywords
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..10000
- 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
Programs
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Haskell
a003667 n = a003667_list !! (n-1) a003667_list = 1 : 5 : ulam 2 5 a003667_list -- Function ulam as defined in A002858. -- Reinhard Zumkeller, Nov 03 2011
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Mathematica
Nest[Append[#, SelectFirst[Union@ Select[Tally@ Map[Total, Select[Permutations[#, {2}], #1 < #2 & @@ # &]], Last@ # == 1 &][[All, 1]], Function[k, FreeQ[#, k]]]] &, {1, 5}, 58] (* Michael De Vlieger, Nov 16 2017 *)
Extensions
Name clarfied by David A. Corneth, Mar 13 2023
Comments