A304274 - OEIS

%I #40 Jul 03 2021 07:59:29

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

%T 1,2,2,1,2,1,1,1,1,1,1,1,2,1,2,2,2,2,2,1,1,2,2,1,2,1,2,2,1,2,1,2,1,1,

%U 2,1,1,2,2,2,2,1,2,2,1,2,2,2,2,2,2,1,2,1,1,1,1,1,2,2,1,2,2,1,2,1,2,2,1,1,2

%N The concatenation of the first n elements is the largest positive even number with n digits when written in base 3/2.

%C This sequence is possible due to the fact that the largest even integers are prefixes of each other.

%C A304272(n) is the largest even integer with n digits.

%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) = A304273(n+1) + 1.

%F From _Alois P. Heinz_, Jun 21 2018: (Start)

%F a(n) = A305498(n+1) -3/2*A305498(n) + 1.

%F Sum_{i=0..n-1} (3/2)^i*a(n-i) = A305497(n). (End)

%e Number 8 in base 3/2 is 212, and it is the largest even integer with 3 digits in base 3/2. Its prefix 21 is 4: the largest even integer with 2 digits in base 3/2.

%p b:= proc(n) option remember; `if`(n=1, 2,

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

%p     end:

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

%p seq(a(n), n=1..120);  # _Alois P. Heinz_, Jun 21 2018

%t b[n_] := b[n] = If[n == 1, 2, Function[t, t + Mod[t, 2]][3/2 b[n-1]]];

%t a[n_] := b[n+1] - 3/2 b[n] + 1;

%t Array[a, 120] (* _Jean-François Alcover_, Dec 13 2018, after _Alois P. Heinz_ *)

%Y Cf. A005428, A070885, A073941, A081848, A024629, A246435, A304024, A304025, A303500, A304272, A304273, A305497, A305498.

%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