A303500 - OEIS

%I #74 Jul 03 2021 07:58:58

%S 2,21,210,2101,21011,210110,2101100,21011000,210110001,2101100011,

%T 21011000110,210110001101,2101100011010,21011000110100,

%U 210110001101001,2101100011010011,21011000110100110,210110001101001101

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

%C a(n) is a prefix of a(n+1).

%C The smallest, not necessarily even, integer in base 3/2 with n digits is a(n-1) with 0 added at the end.

%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) = A024629(A305498(n)). - _R. J. Mathar_, Jun 25 2018

%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.

%p roll32 := proc(L)

%p     local piv,L1 ;

%p     piv := 1;

%p     L1 := subsop(piv=op(piv,L)+1,L) ;

%p     while op(piv,L1) >= 3 do

%p         L1 := [seq(0,i=1..piv), op(piv+1,L1)+1, seq(op(i,L1),i=piv+2..nops(L1))] ;

%p         piv := piv+1 ;

%p     end do:

%p     L1 ;

%p end proc:

%p from32 := proc(L)

%p     add( op(i,L)*(3/2)^(i-1),i=1..nops(L)) ;

%p end proc:

%p A303500 := proc(n)

%p     local dgs ;

%p     dgs := [seq(0,i=1..n-1),1] ;

%p     while not type(from32(dgs),'even') do

%p         dgs := roll32(dgs) ;

%p     end do:

%p     dgs := ListTools[Reverse](dgs) ;

%p     digcatL(%) ;

%p end proc: # _R. J. Mathar_, Jun 25 2018

%Y See A024629 for the base-3/2 expansion of n.

%Y Cf. also A304024, A304025, A070885, A304272, A081848, A246435, A005428, A073941.

%K nonn,base

%O 0,1

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