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The smallest positive even integer that can be represented with n digits in base 3/2.
3

%I #27 Sep 21 2022 01:41:43

%S 2,4,6,10,16,24,36,54,82,124,186,280,420,630,946,1420,2130,3196,4794,

%T 7192,10788,16182,24274,36412,54618,81928,122892,184338,276508,414762,

%U 622144,933216,1399824,2099736,3149604,4724406,7086610,10629916,15944874,23917312

%N The smallest positive even integer that can be represented with n digits in base 3/2.

%H B. Chen, R. Chen, J. Guo, S. Lee et al., <a href="http://arxiv.org/abs/1808.04304">On Base 3/2 and its Sequences</a>, arXiv:1808.04304 [math.NT], 2018.

%F a(n+1) = 2*ceiling(3*a(n)/4).

%F a(n) = 2*A061419(n).

%F a(n) = A305497(n-1) + 2.

%o (Python)

%o from itertools import islice

%o def A305498_gen(): # generator of terms

%o a = 2

%o while True:

%o yield (a<<1)-2

%o a += a>>1

%o A305498_list = list(islice(A305498_gen(),70)) # _Chai Wah Wu_, Sep 20 2022

%Y Cf. A005428, A070885, A073941, A081848, A024629, A246435, A304023, A304024, A304025, A303500, A304272, A304273, A304274, A305497.

%K nonn,base

%O 1,1

%A _Tanya Khovanova_ and PRIMES STEP Senior group, Jun 02 2018