A006638 Restricted postage stamp problem with n denominations and 2 stamps. (Formerly M1088)

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

1,1

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

References

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

Links

Table of n, a(n) for n=1..47.

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).

Example

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

Crossrefs

Cf. A001212.

Sequence in context: A160408 A221707 A186146 * A001212 A364769 A160742

Adjacent sequences: A006635 A006636 A006637 * A006639 A006640 A006641

Keyword

nonn

Author

N. J. A. Sloane.

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

Status

approved