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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)
8
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 (list; graph; refs; listen; history; text; internal format)
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
Steven R. Finch, Ulam s-Additive Sequences [From Steven Finch, Apr 20 2019]
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
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.
Sequence in context: A049468 A187332 A326917 * A091532 A108345 A073629
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
More terms from Jud McCranie
STATUS
approved

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Last modified May 29 08:50 EDT 2024. Contains 372926 sequences. (Running on oeis4.)