A304273 - OEIS

%I #43 Mar 13 2021 00:06:05

%S 2,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,0,0,

%T 0,0,1,1,0,1,0,0,0,0,0,0,0,1,0,1,1,1,1,1,0,0,1,1,0,1,0,1,1,0,1,0,1,0,

%U 0,1,0,0,1,1,1,1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,1,0,1,0,1,1,0,0

%N The concatenation of the first n terms is the smallest positive even number with n digits when written in base 3/2 (cf. A024629).

%C This sequence exists since the smallest even integers (see A303500) are prefixes of each other.

%C Apparently a variant of A205083. - _R. J. Mathar_, Jun 09 2018

%H Michael De Vlieger, <a href="/A304273/b304273.txt">Table of n, a(n) for n = 1..10000</a>

%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 For n>1, a(n) = A304274(n-1) - 1.

%e The number 5 in base 3/2 is 22, and the number 6 is 210. Therefore 210 is the smallest even integer with 3 digits in base 3/2. Its prefix 21 is 4: the smallest even integer with 2 digits in base 3/2.

%p b:= proc(n) option remember; `if`(n<2, 2*n,

%p       (t-> t+irem(t, 2))(b(n-1)*3/2))

%p     end:

%p a:= n-> b(n)-3/2*b(n-1):

%p seq(a(n), n=1..105);  # _Alois P. Heinz_, Jun 21 2018

%t b[n_] := b[n] = If[n < 2, 2*n, Function[t, t + Mod[t, 2]][3/2 b[n - 1]]]; a[n_] := b[n] - 3/2 b[n - 1]; Table[a[n], {n, 1, 105}] (* _Robert P. P. McKone_, Feb 12 2021 *)

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

%Y See also A205083.

%K nonn,base

%O 1,1

%A _Tanya Khovanova_ and PRIMES STEP Senior group, May 09 2018

%E More terms from _Alois P. Heinz_, Jun 21 2018