A304273 The concatenation of the first n terms is the smallest positive even number with n digits when written in base 3/2 (cf. A024629).

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, 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, 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

Offset: 1

Author

Tanya Khovanova and PRIMES STEP Senior group, May 09 2018

Keywords

• nonn
• base

Comments

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

Apparently a variant of A205083. - R. J. Mathar, Jun 09 2018

Examples

			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.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• B. Chen, R. Chen, J. Guo, S. Lee et al., On Base 3/2 and its Sequences, arXiv:1808.04304 [math.NT], 2018.

Crossrefs

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

See also A205083.

Programs

Maple

b:= proc(n) option remember; `if`(n<2, 2*n,
      (t-> t+irem(t, 2))(b(n-1)*3/2))
    end:
a:= n-> b(n)-3/2*b(n-1):
seq(a(n), n=1..105);  # Alois P. Heinz, Jun 21 2018

Mathematica

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 *)

Formula

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

Extensions

More terms from Alois P. Heinz, Jun 21 2018