|
| |
|
|
A006844
|
|
a(1)=4, a(2)=5; thereafter a(n) is smallest number that is greater than a(n-1) and having a unique representation as a(j) + a(k) for j<k.
(Formerly M3245)
|
|
3
|
|
|
|
4, 5, 9, 13, 14, 17, 19, 21, 24, 25, 27, 35, 37, 43, 45, 47, 57, 67, 69, 73, 77, 83, 93, 101, 105, 109, 113, 115, 123, 125, 133, 149, 153, 163, 173, 197, 201, 205, 209, 211, 213, 217, 219, 227, 229, 235, 237, 239
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
This is the 1-additive sequence with base {4,5}. Apart from three extra terms (4, 14, 24) in the initial segment, this breaks up naturally into segments of 32 terms each. [Finch, 1992]. - N. J. A. Sloane, Aug 12 2015
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.
R. K. Guy, Unsolved Problems in Number Theory, Section C4.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
|
|
|
|
FORMULA
|
For n>9, a(n+32) = a(n) + 192. - T. D. Noe, Jan 21 2008
|
|
|
MATHEMATICA
|
s = {4, 5}; n0 = 9; dn = 32; m = 192; Do[ AppendTo[s, n = Last[s]; While[n++; Length[ DeleteCases[ Intersection[s, n - s], n/2, 1, 1]] != 2]; n], {n0 + dn}]; Clear[a]; a[n_] := a[n] = If[n <= n0 + dn, s[[n]], a[n - dn] + m]; Table[a[n], {n, 1, 200}] (* Jean-François Alcover, Apr 03 2013 *)
|
|
|
PROG
|
(Haskell)
a006844 n = a006844_list !! (n-1)
a006844_list = 4 : 5 : ulam 2 5 a006844_list
-- Function ulam as defined in A002858.
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
easy,nonn,nice
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
