A123509 - OEIS

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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).

1, 3, 5, 9, 13, 17, 21, 27, 33, 41, 47, 55 (list; graph; refs; listen; history; 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	`Charles R Greathouse IV, Home Page [in lieu of email address]` `W. D. Smith, More information`
	FORMULA	`a(n) = A001212(n)+1 (conjecture). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 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 (warren.wds(AT)gmail.com), Oct 02 2006`
	EXTENSIONS	`More terms (from Smith's web site) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 08 2006`

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Last modified February 17 06:27 EST 2012. Contains 205998 sequences.