A006638 Restricted postage stamp problem with n denominations and 2 stamps.

2, 4, 8, 12, 16, 20, 26, 32, 40, 44, 54, 64, 72, 80, 92, 104, 116, 128, 140, 152, 164, 180, 196, 212, 228, 244, 262, 280, 298, 316, 338, 360, 382, 404, 426, 448, 470, 492, 514, 536, 562, 588, 614, 644, 674, 704, 734

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

a(n) = largest span (range) attained by a restricted additive 2-basis of length n; an additive 2-basis is restricted if its span is exactly twice its largest element. - Jukka Kohonen, Apr 23 2014

Examples

			a(10)=44: For example, the basis {0, 1, 2, 3, 7, 11, 15, 17, 20, 21, 22} has 10 nonzero elements, and all integers between 0 and 44 can be expressed as sums of two elements of the basis. Currently n=10 is the only known case where A006638 differs from A001212. - _Jukka Kohonen_, Apr 23 2014
		

References

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

Links

• J. Kohonen, A Meet-in-the-Middle Algorithm for Finding Extremal Restricted Additive 2-Bases, J. Integer Seq., 17 (2014), Article 14.6.8.
• J. Kohonen, Early Pruning in the Restricted Postage Stamp Problem, arXiv:1503.03416 [math.NT] preprint (2015).
• S. S. Wagstaff, Jr., Additive h-bases for n, pp. 302-327 of Number Theory Carbondale 1979, Lect. Notes Math. 751 (1982).

Crossrefs

Cf. A001212.

Extensions

Definition improved by Jukka Kohonen, Apr 23 2014

Extended up to a(41) from Kohonen (2014), by Jukka Kohonen, Apr 23 2014

Extended up to a(47) from Kohonen (2015), by Jukka Kohonen, Mar 14 2015