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A123509 Rohrbach's problem: a(n) is the largest integer such that there exists a set of n integers that is a basis of order 2 for (0, 1, ..., a(n)-1). 3
1, 3, 5, 9, 13, 17, 21, 27, 33, 41, 47, 55 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Notation: N[q] = the set of q+1 elements inside {0,1,...,N-1}

REFERENCES

S. Gunturk and M. Nathanson, "A new upper bound for finite additive bases", Acta Arithmetica, Vol. 124, No. 3 (2006).

LINKS

Table of n, a(n) for n=1..12.

W. D. Smith, More information

FORMULA

a(n) = A001212(n)+1 (conjecture). - R. J. Mathar, Oct 08 2006. Comment from Martin Fuller, Mar 18 2009: I agree with this conjecture.

lim inf a(n) / n^2 > 0.2857 lim sup a(n) / n^2 < 0.4789 - Charles R Greathouse IV, Aug 11 2007

EXAMPLE

Example: 8[3]: 0,1,3,4 means {0,1,2,...,8} is covered thus: 0=0+0, 1=0+1, 2=1+1, 3=0+3, 4=0+4=1+3, 5=1+4, 6=3+3, 7=3+4, 8=4+4.

N[q]: set

------------------------------

3[2]: 0,1,

4[3]: 0,1,2,

5[3]: 0,1,2,

6[3]: 0,2,3,

7[4]: 0,1,2,3,

8[4]: 0,1,3,4,

9[4]: 0,1,3,4,

10[5]: 0,1,2,4,5,

11[5]: 0,1,2,4,5,

12[5]: 0,1,3,5,6,

13[5]: 0,1,3,5,6,

14[6]: 0,1,2,4,6,7,

15[6]: 0,1,2,4,6,7,

16[6]: 0,1,3,5,7,8,

17[6]: 0,1,3,5,7,8,

18[6]: 0,2,3,7,8,10,

19[7]: 0,1,2,4,6,8,9,

20[7]: 0,1,3,5,7,9,10,

21[7]: 0,1,3,5,7,9,10,

22[7]: 0,2,3,7,8,10,11,

23[8]: 0,1,2,4,6,8,10,11,

24[8]: 0,1,3,5,7,9,11,12,

25[8]: 0,1,3,5,7,9,11,12,

26[8]: 0,2,3,7,8,10,12,13,

27[8]: 0,1,3,4,9,10,12,13,

28[8]: 0,2,3,7,8,12,13,15,

29[9]: 0,1,3,5,7,9,11,13,14,

30[9]: 0,2,3,7,8,10,12,14,15,

31[9]: 0,1,3,4,9,10,12,14,15,

32[9]: 0,2,3,7,8,12,13,15,16,

CROSSREFS

Cf. A001212, A008932.

Sequence in context: A050556 A138008 A063954 * A196094 A063915 A183859

Adjacent sequences:  A123506 A123507 A123508 * A123510 A123511 A123512

KEYWORD

hard,more,nonn

AUTHOR

Warren D. Smith, Oct 02 2006

EXTENSIONS

More terms (from Smith's web site) from R. J. Mathar, Oct 08 2006

STATUS

approved

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Last modified March 26 06:49 EDT 2017. Contains 284111 sequences.