A001857 a(1)=2, a(2)=3; for n >= 3, a(n) is smallest number that is uniquely of the form a(j) + a(k) with 1 <= j < k < n. (Formerly M0634 N0231)

2, 3, 5, 7, 8, 9, 13, 14, 18, 19, 24, 25, 29, 30, 35, 36, 40, 41, 46, 51, 56, 63, 68, 72, 73, 78, 79, 83, 84, 89, 94, 115, 117, 126, 153, 160, 165, 169, 170, 175, 176, 181, 186, 191, 212, 214, 230, 235, 240, 245, 266, 273, 278, 283, 288, 325, 331, 332, 337, 342

Offset

1,1

Comments

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

A plot of the first 10^6 terms shows a nearly straight line having a slope of about 11.1. In contrast to A002858, this sequence has many consecutive numbers; of the first 10^6 terms, consecutive numbers appear 141674 times! - T. D. Noe, Jan 21 2008

References

S. R. Finch, Patterns in 1-additive sequences, Experimental Mathematics 1 (1992), 57-63.

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 145-151.

R. K. Guy, Unsolved Problems in Number Theory, Section C4.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

S. M. Ulam, Problems in Modern Mathematics, Wiley, NY, 1960, p. ix.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Steven R. Finch, Ulam s-Additive Sequences [From Steven Finch, Apr 20 2019]

J. Cassaigne and S. R. Finch, A class of 1-additive sequences and additive recurrences

N. J. A. Sloane, Handwritten notes on Self-Generating Sequences, 1970 (note that A1148 has now become A005282)

Eric Weisstein's World of Mathematics, Ulam Sequence

Wikipedia, Ulam number

Index entries for Ulam numbers

Mathematica

s = {2, 3}; Do[ AppendTo[s, n = Last[s]; While[n++; Length[ DeleteCases[ Intersection[s, n-s], n/2, 1, 1]] != 2]; n], {100}]; s (* Jean-François Alcover, Sep 08 2011 *)

Prog

(Haskell)
a001857 n = a001857_list !! (n-1)
a001857_list = 2 : 3 : ulam 2 3 a001857_list
-- Function ulam as defined in A002858.
-- Reinhard Zumkeller, Nov 03 2011

Crossrefs

Cf. A100729.

Cf. A199122, A199123.

Sequence in context: A049468 A187332 A326917 * A091532 A108345 A073629

Adjacent sequences: A001854 A001855 A001856 * A001858 A001859 A001860

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from Jud McCranie

Status

approved