A383500 Positive integers that contain the digit 9, or an odd digit d immediately preceded by a digit <= d.

9, 11, 13, 15, 17, 19, 23, 25, 27, 29, 33, 35, 37, 39, 45, 47, 49, 55, 57, 59, 67, 69, 77, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 103, 105, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 123, 125, 127, 129, 130, 131, 132, 133, 134, 135, 136, 137

Offset: 1

Author

Paolo Xausa, Apr 29 2025

Keywords

• nonn
• base
• easy

Comments

Conjecture: these are the numbers missing from A382935.

Theorem: This sequence is the complement of A382935. - Quinn Savitt, May 08 2025

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Quinn Savitt, Proof that A383500 is the Complement of A382935

Crossrefs

Cf. A382935, A383501 (complement).

Cf. A347298, A382464, A382623, A382937, A383061, A383245, A383247, A383249.

Programs

Mathematica

A383500Q[k_] := MemberQ[#, 9] || MemberQ[Partition[#, 2, 1], {i_, j_?OddQ} /; i <= j] & [IntegerDigits[k]];
Select[Range[200], A383500Q]

Python

def ok(n):
    s = str(n)
    return "9" in s or any(d in "13579" and 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