A303500 The smallest positive even integer that can be written with n digits in base 3/2.

2, 21, 210, 2101, 21011, 210110, 2101100, 21011000, 210110001, 2101100011, 21011000110, 210110001101, 2101100011010, 21011000110100, 210110001101001, 2101100011010011, 21011000110100110, 210110001101001101

Offset

0,1

Comments

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

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

Links

Table of n, a(n) for n=0..17.

B. Chen, R. Chen, J. Guo, S. Lee et al., On Base 3/2 and its Sequences, arXiv:1808.04304 [math.NT], 2018.

Formula

a(n) = A024629(A305498(n)). - R. J. Mathar, Jun 25 2018

Example

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.

Maple

roll32 := proc(L)
    local piv, L1 ;
    piv := 1;
    L1 := subsop(piv=op(piv, L)+1, L) ;
    while op(piv, L1) >= 3 do
        L1 := [seq(0, i=1..piv), op(piv+1, L1)+1, seq(op(i, L1), i=piv+2..nops(L1))] ;
        piv := piv+1 ;
    end do:
    L1 ;
end proc:
from32 := proc(L)
    add( op(i, L)*(3/2)^(i-1), i=1..nops(L)) ;
end proc:
A303500 := proc(n)
    local dgs ;
    dgs := [seq(0, i=1..n-1), 1] ;
    while not type(from32(dgs), 'even') do
        dgs := roll32(dgs) ;
    end do:
    dgs := ListTools[Reverse](dgs) ;
    digcatL(%) ;
end proc: # R. J. Mathar, Jun 25 2018

Crossrefs

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

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

Sequence in context: A068070 A085953 A225614 * A037527 A131584 A037736

Adjacent sequences: A303497 A303498 A303499 * A303501 A303502 A303503

Keyword

nonn,base

Author

Tanya Khovanova and PRIMES STEP Senior group, May 09 2018

Status

approved