A377912 Numbers such that every even digit except the last is immediately followed by a strictly larger digit.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117

Offset: 1

Author

N. J. A. Sloane, Nov 27 2024, with thanks to Paolo Xausa for correcting the initial definition

Keywords

• nonn
• base

Comments

In other words, numbers that do not contain a pair of successive digits i, j where i is even and j <= i.

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Sela Fried, Even-up words and their variants, arXiv:2505.14196 [math.CO], 2025.

Crossrefs

The complement of A347298. Cf. A342042, A377914, A377917, A377918.

Programs

Mathematica

A377912Q[k_] := FreeQ[Partition[IntegerDigits[k], 2, 1], {i_?EvenQ, j_} /; j <= i];
Select[Range[0, 200], A377912Q] (* Paolo Xausa, Mar 17 2025 *)

Python

def ok(n):
    s = str(n)
    return not any(s[i] in "2468" and s[i+1] <= s[i] for i in range(len(s)-1))
print([k for k in range(0, 118) if ok(k)]) # Michael S. Branicky, Nov 28 2024

Extensions

Added 0 to match A342042, and replaced negative definition by a positive one. - N. J. A. Sloane, Nov 29 2024