A003670 a(n) is smallest number which is uniquely a(j)+a(k).

4, 7, 11, 15, 18, 19, 23, 25, 27, 31, 32, 33, 35, 41, 47, 49, 55, 57, 61, 63, 75, 87, 89, 91, 105, 119, 121, 125, 129, 133, 139, 147, 153, 161, 185, 189, 203, 206, 213, 225, 233, 235, 241, 243, 251, 257, 259, 265, 273, 281, 285, 293, 295, 303, 305, 307, 309, 317

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn

Comments

Sequence is periodic mod 11301098.

An Ulam-type sequence - see A002858 for many further references, comments, etc. - T. D. Noe, Jan 21 2008

References

• Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 145-151.
• 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
• Steven R. Finch, Stolarsky-Harborth Constant [Broken link]
• Steven R. Finch, Stolarsky-Harborth Constant [From the Wayback machine]
• Steven 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

Programs

Haskell

a003670 n = a003670_list !! (n-1)
a003670_list = 4 : 7 : ulam 2 7 a003670_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]]]] &, {4, 7}, 56] (* Michael De Vlieger, Nov 16 2017 *)