A383245 Nonnegative integers that contain the digit 0, or an even digit d immediately followed by a digit >= d.

0, 10, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 40, 44, 45, 46, 47, 48, 49, 50, 60, 66, 67, 68, 69, 70, 80, 88, 89, 90, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 120, 122, 123, 124, 125, 126, 127, 128, 129, 130, 140, 144, 145, 146, 147, 148, 149, 150, 160, 166

Offset: 1

Author

Paolo Xausa, Apr 20 2025

Keywords

• nonn
• base
• easy

Comments

Conjecture: these are the numbers missing from A342043.

Links

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

Crossrefs

Cf. A342043, A383246 (complement).

Cf. A347298, A382464, A382623, A382937, A383061, A383247, A383249, A383500.

Programs

Mathematica

A383245Q[k_] := MemberQ[#, 0] || MemberQ[Partition[#, 2, 1], {i_?EvenQ, j_} /; j >= i] & [IntegerDigits[k]];
Select[Range[0, 200], A383245Q]

Python

def ok(n):
    if n%10 == 0: return True
    s = str(n)
    return any(d in "02468" and s[i]>=d for i, d in enumerate(s, 1) if i < len(s))
print([k for k in range(167) if ok(k)]) # Michael S. Branicky, Apr 28 2025