A382624 Positive integers such that every even digit except the leftmost is immediately preceded by a larger digit.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 19, 20, 21, 23, 25, 27, 29, 30, 31, 32, 33, 35, 37, 39, 40, 41, 42, 43, 45, 47, 49, 50, 51, 52, 53, 54, 55, 57, 59, 60, 61, 62, 63, 64, 65, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90

Offset: 1

Author

Paolo Xausa, Apr 01 2025

Keywords

• nonn
• base
• easy

Comments

Conjecture: these are the terms of A382621, sorted.

Links

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

Crossrefs

Cf. A377912, A382465, A382621, A382623 (complement).

Programs

Mathematica

A382624Q[k_] := FreeQ[Partition[IntegerDigits[k], 2, 1], {i_, j_?EvenQ} /; i <= j];
Select[Range[100], A382624Q]

Python

def ok(n):
    s = str(n)
    return all(s[i+1] < s[i] for i in range(len(s)-1) if s[i+1] in "02468")
print([k for k in range(1, 91) if ok(k)]) # Michael S. Branicky, Apr 03 2025