A306105 Numbers with digits in {0,1,2} such that every other digit is strictly less than its neighbors.

0, 1, 2, 10, 20, 21, 101, 102, 201, 202, 212, 1010, 1020, 1021, 2010, 2020, 2021, 2120, 2121, 10101, 10102, 10201, 10202, 10212, 20101, 20102, 20201, 20202, 20212, 21201, 21202, 21212, 101010, 101020, 101021, 102010, 102020, 102021, 102120, 102121

Offset

1,3

Comments

Terms of A032858 written in base 3.

There are A000045(n+2) terms with n digits (where 0 is taken to have no digits), so the first term with n digits is at index A000071(n+3). See A032858 for the proof.

Links

Table of n, a(n) for n=1..40.

Formula

a(n) = A007089(A032858(n)).

Prog

(PARI) {A=[0, 1, 2]; F=[1, 1]; for(n=0, 4, F=[F[2], vecsum(F)]; for(k=1, 3, T=max(k*10, 21)*10^n; A=concat(A, apply(t->t+T, A[F[2]-1+if(k>2, F*[2, -1]~)..vecsum(F)-2])))); A}

Crossrefs

Cf. A306106 .. A306111 and A297147: analog for bases 3..9 and 10.

Cf. A000045 (Fibonacci), A000071(n) = Sum(k=0..n-2,A45(k)) = A000045(n)-1.

Cf. A032858 and A032859 .. A032865 for other bases 3..10.

Sequence in context: A009342 A357486 A350508 * A038103 A307254 A293725

Adjacent sequences: A306102 A306103 A306104 * A306106 A306107 A306108

Keyword

nonn,base

Author

M. F. Hasler, Oct 05 2018

Status

approved