A382465 Positive integers such that every even digit except the first is immediately preceded by a smaller digit.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 31, 33, 34, 35, 36, 37, 38, 39, 41, 43, 45, 46, 47, 48, 49, 51, 53, 55, 56, 57, 58, 59, 61, 63, 65, 67, 68, 69, 71, 73, 75, 77, 78, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99

Offset: 1

Author

Paolo Xausa, Mar 28 2025

Keywords

• nonn
• base
• easy

Comments

Conjecture: these are the terms of A382462, sorted.

Links

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

Crossrefs

Cf. A382462, A382464 (complement).

Cf. A377912, A382624, A382938, A383062, A383246, A383248, A383250, A383501.

Programs

Mathematica

A382465Q[k_] := FreeQ[Partition[IntegerDigits[k], 2, 1], {i_, j_?EvenQ} /; i >= j];
Select[Range[100], A382465Q]

Python

def ok(n):
    s = str(n)
    return n and all(d not in "02468" or s[i-1] 0)
print([k for k in range(100) if ok(k)]) # Michael S. Branicky, Apr 30 2025