A003668 a(n) is smallest number which is uniquely a(j)+a(k), j<k. (Formerly M1731)

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

1,1

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