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

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn

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

Crossrefs

Cf. A100729.

Programs

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

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 *)

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

Formula

Akeran gives a formula.

For n>7, a(n+26)=a(n)+126. - T. D. Noe, Jan 21 2008