A306111 Numbers with digits in {0,...,8} such that every other digit is strictly less than its neighbors.

0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 20, 21, 30, 31, 32, 40, 41, 42, 43, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 85, 86, 87, 101, 102, 103, 104, 105, 106, 107, 108, 201, 202, 203, 204, 205, 206, 207, 208, 212, 213, 214, 215, 216, 217, 218, 301, 302, 303, 304, 305, 306, 307

Offset

1,3

Comments

Terms of A032864 written in base 9.

Links

Table of n, a(n) for n=1..75.

Formula

a(n) = A007095(A032864(n)).

Numbers in A297147 having no digit 9: Intersection of A297147 with A007095.

Example

There are 1+2+3+4+5+6+7+8 = 9*4 = 36 terms with 2 digits.
We obtain the 3-digit terms by appending to each of these the 1-digit terms starting with a digit larger than the last digit of the prefix: 10.{1..8}, 20.{1..8}, 21.{2..8}, 30.{1..8}, ..., 86.{7..8}, 87.{8}.
We obtain the 4-digit terms by appending to each of the 2 digit terms, the 2-digit terms starting with a digit larger than the last digit of the prefix: 10.{10,...,87}, 20.{10,...,87}, 21.{20,...,87}, 30.{10,...,87}, ..., 86.{70,...,87}, 87.{80..87}.
That way we obtain all terms with n digits by taking the 2-digit terms and appending to each of these the suitable subsequence of n-2 digit terms.

Prog

(PARI) A(Nmax=100, K=8, A=[0..K], i=vector(2*K, i, max(1, i-K+1)), c(T, v)=apply(t->t+T, v))={for(n=0, oo, for(k=10, K*11-1, if(k%10<k\10, k%10|| i=concat(i, 1+#A); A=concat(A, c(k*10^n, A[i[K*n+k%10+1]..i[K*n+K+1]-1])); #A<Nmax||return(A))))}

Crossrefs

Cf. A306105 .. A306110 and A297147: analog for bases 3..8 and 10.

Cf. A032864 and A032858 .. A032865 for other bases 3..10.

Sequence in context: A271952 A033073 A369406 * A039172 A044958 A297145

Adjacent sequences: A306108 A306109 A306110 * A306112 A306113 A306114

Keyword

nonn,base

Author

M. F. Hasler, Oct 05 2018

Status

approved