A383247 Positive integers that contain the digit 9, or an odd digit d immediately followed by a digit <= d.

9, 10, 11, 19, 29, 30, 31, 32, 33, 39, 49, 50, 51, 52, 53, 54, 55, 59, 69, 70, 71, 72, 73, 74, 75, 76, 77, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 129, 130, 131, 132, 133

Offset: 1

Author

Paolo Xausa, Apr 25 2025

Keywords

• nonn
• base
• easy

Comments

Conjecture: these are the numbers missing from A342044.

Links

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

Crossrefs

Cf. A342044, A383248 (complement).

Cf. A347298, A382464, A382623, A382937, A383061, A383245, A383249.

Programs

Mathematica

A383247Q[k_] := MemberQ[#, 9] || MemberQ[Partition[#, 2, 1], {i_?OddQ, j_} /; j <= i] & [IntegerDigits[k]];
Select[Range[200], A383247Q]

Python

def ok(n):
    s = str(n)
    return "9" in s or any(d in "13579" and s[i]<=d for i, d in enumerate(s, 1) if i < len(s))
print([k for k in range(134) if ok(k)]) # Michael S. Branicky, Apr 28 2025