A003670 a(n) is smallest number which is uniquely a(j)+a(k). (Formerly M3303)

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

1,1

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A190774 A267049 A310735 * A084390 A101741 A247432

Adjacent sequences: A003667 A003668 A003669 * A003671 A003672 A003673

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Status

approved