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

1,3

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A059962 A057605 A247759 * A326872 A396694 A110548

Adjacent sequences: A377909 A377910 A377911 * A377913 A377914 A377915

Keyword

nonn,base

Author

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

Extensions

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

Status

approved