A383249 -id:A383249 - cp's OEIS frontend

A382464 Positive integers that contain an even digit d immediately preceded by a digit >= d.

10, 20, 22, 30, 32, 40, 42, 44, 50, 52, 54, 60, 62, 64, 66, 70, 72, 74, 76, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 120, 122, 130, 132, 140, 142, 144, 150, 152, 154, 160, 162, 164, 166, 170, 172, 174, 176, 180

Offset: 1

Paolo Xausa, Mar 28 2025

Conjecture: these are the numbers missing from A382462.

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

Cf. A382462, A382465 (complement).

Cf. A347298, A382623, A382937, A383061, A383245, A383247, A383249, A383500.

A382464Q[k_] := MemberQ[Partition[IntegerDigits[k], 2, 1], {i_, j_?EvenQ} /; i >= j];
Select[Range[200], A382464Q]

def ok(n):
    s = str(n)
    return any(d in "02468" and s[i-1]>=d for i, d in enumerate(s) if i > 0)
print([k for k in range(181) if ok(k)]) # Michael S. Branicky, Apr 30 2025

A383061 Positive integers that contain an odd digit d immediately preceded by a digit >= d.

Original entry on oeis.org

11, 21, 31, 33, 41, 43, 51, 53, 55, 61, 63, 65, 71, 73, 75, 77, 81, 83, 85, 87, 91, 93, 95, 97, 99, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 131, 133, 141, 143, 151, 153, 155, 161, 163, 165, 171, 173, 175, 177, 181, 183, 185, 187, 191, 193, 195, 197, 199

Offset: 1

Paolo Xausa, Apr 18 2025

Conjecture: these are the numbers missing from A383059.

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

Cf. A383059, A383062 (complement).

Cf. A347298, A382464, A382623, A382937, A383245, A383247, A383249, A383500.

A383061Q[k_] := MemberQ[Partition[IntegerDigits[k], 2, 1], {i_, j_?OddQ} /; i >= j];
Select[Range[200], A383061Q]

def ok(n):
    s = str(n)
    return any(s[i] <= s[i-1] for i in range(1, len(s)) if s[i] in "13579")
print([k for k in range(200) if ok(k)]) # Michael S. Branicky, Apr 19 2025

A382937 Positive integers that contain an odd digit d immediately preceded by a digit <= d.

Original entry on oeis.org

11, 13, 15, 17, 19, 23, 25, 27, 29, 33, 35, 37, 39, 45, 47, 49, 55, 57, 59, 67, 69, 77, 79, 89, 99, 101, 103, 105, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 123, 125, 127, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 145, 147, 149, 150

Offset: 1

Paolo Xausa, Apr 14 2025

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

Cf. A382938 (complement).

Cf. A347298, A382464, A382623, A383061, A383245, A383247, A383249, A383500.

A382937Q[k_] := MemberQ[Partition[IntegerDigits[k], 2, 1], {i_, j_?OddQ} /; i <= j];
Select[Range[200], A382937Q]

def ok(n):
    s = str(n)
    return any(s[i+1] >= s[i] for i in range(len(s)-1) if s[i+1] in "13579")
print([k for k in range(1, 151) if ok(k)]) # Michael S. Branicky, Apr 14 2025

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

Original entry on oeis.org

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

Paolo Xausa, Apr 20 2025

Conjecture: these are the numbers missing from A342043.

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

Cf. A342043, A383246 (complement).

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

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

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

A383247 Positive integers that contain the digit 9, or an odd digit d immediately followed by a digit <= d.

Original entry on oeis.org

9, 10, 11, 19, 29, 30, 31, 32, 33, 39, 49, 50, 51, 52, 53, 54, 55, 59, 69, 70, 71, 72, 73, 74, 75, 76, 77, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 129, 130, 131, 132, 133

Offset: 1

Paolo Xausa, Apr 25 2025

Conjecture: these are the numbers missing from A342044.

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

Cf. A342044, A383248 (complement).

Cf. A347298, A382464, A382623, A382937, A383061, A383245, A383249.

A383247Q[k_] := MemberQ[#, 9] || MemberQ[Partition[#, 2, 1], {i_?OddQ, j_} /; j <= i] & [IntegerDigits[k]];
Select[Range[200], A383247Q]

def ok(n):
    s = str(n)
    return "9" in s or any(d in "13579" and s[i]<=d for i, d in enumerate(s, 1) if i < len(s))
print([k for k in range(134) if ok(k)]) # Michael S. Branicky, Apr 28 2025

A383250 Nonnegative integers not ending with the digit 1 and such that every odd digit except the rightmost is immediately followed by a smaller digit.

Original entry on oeis.org

0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 100, 102, 103

Offset: 1

Paolo Xausa, Apr 26 2025

Conjecture: these are the terms of A342045, sorted.
From Quinn Savitt, Apr 29 2025: (Start)
Theorem: These are the terms of A342045, sorted.
The proof formally defines an extendibility condition: a finite set of selected numbers remains extendible if, for every finite subset, there exists a new number satisfying the "odd digit implies next smaller digit" rule and not ending in 1.
Using induction and monotonicity of extendibility, it follows that every number satisfying these conditions eventually appears in the greedy construction of A342045. This implies that the sequence is a sorted version of A342045. (End)

Paolo Xausa, Table of n, a(n) for n = 1..10000
Quinn Savitt, Formal proof that A383250 = sorted(A342045)

Cf. A342045, A383249 (complement).

Cf. A377912, A382465, A382624, A383062, A382938, A383246, A383248.

A383250Q[k_] := Last[#] != 1 && FreeQ[Partition[#, 2, 1], {i_?OddQ, j_} /; j >= i] & [IntegerDigits[k]];
Select[Range[0, 200], A383250Q]

def ok(n):
    if n%10 == 1: return False
    s = str(n)
    return all(d in "02468" or s[i]Michael S. Branicky, Apr 28 2025

A383500 Positive integers that contain the digit 9, or an odd digit d immediately preceded by a digit <= d.

Original entry on oeis.org

9, 11, 13, 15, 17, 19, 23, 25, 27, 29, 33, 35, 37, 39, 45, 47, 49, 55, 57, 59, 67, 69, 77, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 103, 105, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 123, 125, 127, 129, 130, 131, 132, 133, 134, 135, 136, 137

Offset: 1

Paolo Xausa, Apr 29 2025

Conjecture: these are the numbers missing from A382935.

Theorem: This sequence is the complement of A382935. - Quinn Savitt, May 08 2025

Paolo Xausa, Table of n, a(n) for n = 1..10000
Quinn Savitt, Proof that A383500 is the Complement of A382935

Cf. A382935, A383501 (complement).

Cf. A347298, A382464, A382623, A382937, A383061, A383245, A383247, A383249.

A383500Q[k_] := MemberQ[#, 9] || MemberQ[Partition[#, 2, 1], {i_, j_?OddQ} /; i <= j] & [IntegerDigits[k]];
Select[Range[200], A383500Q]

def ok(n):
    s = str(n)
    return "9" in s or any(d in "13579" and s[i-1]<=d for i, d in enumerate(s) if i > 0)
print([k for k in range(134) if ok(k)]) # Michael S. Branicky, Apr 29 2025

cp's OEIS Frontend

A382464 Positive integers that contain an even digit d immediately preceded by a digit >= d.

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A383061 Positive integers that contain an odd digit d immediately preceded by a digit >= d.

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A382937 Positive integers that contain an odd digit d immediately preceded by a digit <= d.

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

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A383247 Positive integers that contain the digit 9, or an odd digit d immediately followed by a digit <= d.

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A383250 Nonnegative integers not ending with the digit 1 and such that every odd digit except the rightmost is immediately followed by a smaller digit.

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Mathematica

Python

A383500 Positive integers that contain the digit 9, or an odd digit d immediately preceded by a digit <= d.

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Mathematica

Python