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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. 0

%I #13 Jul 23 2019 04:22:39

%S 1,5,21,150

%N 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.

%C Conjecture: The next terms are a(5) = 2581 and a(6) = 27438. - _Eric Rowland_, Jul 22 2019

%H Melvyn B. Nathanson, <a href="https://doi.org/10.1142/S1793042111004940">Problems in additive number theory, iv: Nets in groups and shortest length g-adic representations, and minimal additive complements</a>, Int. J. Number Theory 7, (2011), 1999-2017.

%H Melvyn B. Nathanson, <a href="https://arxiv.org/abs/1101.0786">Geometric group theory and arithmetic diameter</a>, arXiv:1101.0786 [math.NT], 2011.

%H Satyanand Singh, <a href="https://academicworks.cuny.edu/gc_etds/112">Special Representations, Nathanson's Lambda Sequences and Explicit Bounds</a>, Ph.D. Dissertation, CUNY Academic Works, 2014.

%H Satyanand Singh, <a href="https://arxiv.org/abs/1902.08814">Limit points of Nathanson's Lambda sequences</a>, arXiv:1902.08814 [math.NT], 2019.

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

%K nonn,more

%O 1,2

%A _Michel Marcus_, Feb 26 2019

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Last modified April 19 18:05 EDT 2024. Contains 371798 sequences. (Running on oeis4.)