A344892 Loxton-van der Poorten sequence: base-4 representation contains only -1, 0, +1, converted to ordinary base-4 digits 0,1,2,3.

0, 1, 3, 10, 11, 23, 30, 31, 33, 100, 101, 103, 110, 111, 223, 230, 231, 233, 300, 301, 303, 310, 311, 323, 330, 331, 333, 1000, 1001, 1003, 1010, 1011, 1023, 1030, 1031, 1033, 1100, 1101, 1103, 1110, 1111, 2223, 2230, 2231, 2233, 2300, 2301, 2303, 2310, 2311

Offset: 0

Author

Kevin Ryde, Jun 01 2021

Keywords

• nonn
• easy
• base

Comments

Loxton and van der Poorten's morphism (see A344893), or the way -1 digits cause borrows, shows that this sequence is base 4 digit strings with no digit pair 12, 13, 20, or 21, and least significant digit not 2.

The least significant digit can be any of 0,1,3, then each successive higher digit has three choices: 0,1,3 above a 0 or 1, or 0,2,3 above a 2 or 3. This allows a(n) to be calculated by mapping from the ternary digits of n to these choices, from least to most significant digit.

Links

• Kevin Ryde, Table of n, a(n) for n = 0..6561

Crossrefs

Cf. A006288 (decimal), A344893 (morphism), A007090 (base 4).

Programs

PARI

a(n) = my(v=digits(n,3),prev=0); forstep(i=#v,1,-1, prev=(v[i]+=(v[i]>(prev<2)))); fromdigits(v);

Formula

a(n) = A007090(A006288(n)).