A306589 a(n) is the smallest positive integer that can be written as the sum or difference of exactly n but no fewer powers of 2 and 3.

1, 5, 21, 150

Offset

1,2

Comments

Conjecture: The next terms are a(5) = 2581 and a(6) = 27438. - Eric Rowland, Jul 22 2019

Links

Table of n, a(n) for n=1..4.

Melvyn B. Nathanson, Problems in additive number theory, iv: Nets in groups and shortest length g-adic representations, and minimal additive complements, Int. J. Number Theory 7, (2011), 1999-2017.

Melvyn B. Nathanson, Geometric group theory and arithmetic diameter, arXiv:1101.0786 [math.NT], 2011.

Satyanand Singh, Special Representations, Nathanson's Lambda Sequences and Explicit Bounds, Ph.D. Dissertation, CUNY Academic Works, 2014.

Satyanand Singh, Limit points of Nathanson's Lambda sequences, arXiv:1902.08814 [math.NT], 2019.

Crossrefs

Cf. A000079 (powers of 2), A000244 (powers of 3).

Sequence in context: A220378 A230645 A228113 * A221513 A284231 A182825

Adjacent sequences: A306586 A306587 A306588 * A306590 A306591 A306592

Keyword

nonn,more

Author

Michel Marcus, Feb 26 2019

Status

approved