A383501 Nonnegative integers without the digit 9 such that every odd digit except the leftmost is immediately preceded by a larger digit.

0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 18, 20, 21, 22, 24, 26, 28, 30, 31, 32, 34, 36, 38, 40, 41, 42, 43, 44, 46, 48, 50, 51, 52, 53, 54, 56, 58, 60, 61, 62, 63, 64, 65, 66, 68, 70, 71, 72, 73, 74, 75, 76, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 100, 102, 104, 106, 108

Offset: 1

Author

Paolo Xausa, Apr 29 2025

Keywords

• nonn
• base
• easy

Comments

Conjecture: these are the terms of A382935, sorted.

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A382935, A383500 (complement).

Cf. A377912, A382465, A382624, A382938, A383062, A383246, A383248, A383250.

Programs

Mathematica

A383501Q[k_] := FreeQ[#, 9] && FreeQ[Partition[#, 2, 1], {i_, j_?OddQ} /; i <= j] & [IntegerDigits[k]];
Select[Range[0, 200], A383501Q]

Python

def ok(n):
    s = str(n)
    return "9" not in s and all(d not in "13579" or s[i-1]>d for i, d in enumerate(s) if i > 0)
print([k for k in range(134) if ok(k)]) # Michael S. Branicky, Apr 29 2025