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

0,3

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

Formula

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

Prog

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

Crossrefs

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

Sequence in context: A073108 A352776 A255160 * A357555 A078306 A136815

Adjacent sequences: A344889 A344890 A344891 * A344893 A344894 A344895

Keyword

nonn,easy,base

Author

Kevin Ryde, Jun 01 2021

Status

approved