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. (Formerly M3746)

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

1,2

Comments

An Ulam-type sequence - see A002858 for many further references, comments, etc.

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A121542 A182306 A023379 * A138469 A089362 A333532

Adjacent sequences: A003664 A003665 A003666 * A003668 A003669 A003670

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Extensions

Name clarfied by David A. Corneth, Mar 13 2023

Status

approved