A383500 -id:A383500 - 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

A382935 Lexicographically earliest sequence of distinct nonnegative integers such that if a digit d in the digit stream (ignoring commas) is odd, the previous digit is > d.

Original entry on oeis.org

0, 2, 1, 4, 3, 6, 5, 8, 7, 10, 20, 21, 22, 12, 14, 16, 18, 24, 26, 28, 30, 40, 41, 42, 43, 44, 31, 46, 32, 48, 34, 36, 38, 50, 60, 61, 62, 63, 64, 65, 66, 51, 68, 52, 80, 81, 82, 83, 84, 85, 86, 53, 87, 54, 88, 56, 58, 70, 200, 202, 100, 204, 102, 104, 106, 108, 71, 206, 120, 208

Offset: 1

Paolo Xausa, Apr 14 2025

Could be summarized as "odd digit, previous bigger". A variant of A342042.

No term contains the digit 9.

Paolo Xausa, Table of n, a(n) for n = 1..10000
Paolo Xausa, Color scatterplot of the first 50000 terms

Similar sequences: A342042, A342043, A342044, A342045, A382462, A382621, A383059.

Cf. A382936, A382939, A383500, A383501.

A382935list[nmax_] := Module[{a, s, invQ, fu = 1},
  invQ[k_] := invQ[k] = (If[#, s[k] = #]; #) & [MemberQ[Partition[IntegerDigits[k], 2, 1], {i_, j_?OddQ} /; i <= j]];
  s[_] := False; s[0] = True;
  NestList[(a = fu; While[s[a] || invQ[a] || invQ[# + First[IntegerDigits[a]]], a++] & [Max[Mod[#, 10], 1]*10]; While[s[fu], fu++]; s[a] = True; a) &, 0, nmax - 1]];
A382935list[100]

from itertools import count, islice
def cond(s):
    return all(s[i+1] < s[i] for i in range(len(s)-1) if s[i+1] in "13579")
def agen(): # generator of terms
    an, seen, s, m = 0, {0}, "0", 1
    while True:
        yield an
        an = next(k for k in count(m) if k not in seen and cond(s[-1]+str(k)))
        seen.add(an); s += str(an)
        while m in seen or not cond(str(m)): m += 1
print(list(islice(agen(), 70))) # Michael S. Branicky, Apr 14 2025

A383501 Nonnegative integers without the digit 9 such that every odd digit except the leftmost is immediately preceded by a larger digit.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 18, 20, 21, 22, 24, 26, 28, 30, 31, 32, 34, 36, 38, 40, 41, 42, 43, 44, 46, 48, 50, 51, 52, 53, 54, 56, 58, 60, 61, 62, 63, 64, 65, 66, 68, 70, 71, 72, 73, 74, 75, 76, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 100, 102, 104, 106, 108

Offset: 1

Paolo Xausa, Apr 29 2025

Conjecture: these are the terms of A382935, sorted.

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

Cf. A382935, A383500 (complement).

Cf. A377912, A382465, A382624, A382938, A383062, A383246, A383248, A383250.

A383501Q[k_] := FreeQ[#, 9] && FreeQ[Partition[#, 2, 1], {i_, j_?OddQ} /; i <= j] & [IntegerDigits[k]];
Select[Range[0, 200], A383501Q]

def ok(n):
    s = str(n)
    return "9" not in s and all(d not in "13579" or 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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A382935 Lexicographically earliest sequence of distinct nonnegative integers such that if a digit d in the digit stream (ignoring commas) is odd, the previous digit is > d.

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A383501 Nonnegative integers without the digit 9 such that every odd digit except the leftmost is immediately preceded by a larger digit.

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Python