A382464 -id:A382464 - cp's OEIS frontend

A382465 Positive integers such that every even digit except the first is immediately preceded by a smaller digit.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 31, 33, 34, 35, 36, 37, 38, 39, 41, 43, 45, 46, 47, 48, 49, 51, 53, 55, 56, 57, 58, 59, 61, 63, 65, 67, 68, 69, 71, 73, 75, 77, 78, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99

Offset: 1

Paolo Xausa, Mar 28 2025

Conjecture: these are the terms of A382462, sorted.

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

Cf. A382462, A382464 (complement).

Cf. A377912, A382624, A382938, A383062, A383246, A383248, A383250, A383501.

A382465Q[k_] := FreeQ[Partition[IntegerDigits[k], 2, 1], {i_, j_?EvenQ} /; i >= j];
Select[Range[100], A382465Q]

def ok(n):
    s = str(n)
    return n and all(d not in "02468" or s[i-1] 0)
print([k for k in range(100) if ok(k)]) # Michael S. Branicky, Apr 30 2025

A382623 Positive integers that contain an even digit d immediately preceded by a digit <= d.

Original entry on oeis.org

12, 14, 16, 18, 22, 24, 26, 28, 34, 36, 38, 44, 46, 48, 56, 58, 66, 68, 78, 88, 100, 102, 104, 106, 108, 112, 114, 116, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 134, 136, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 156, 158, 160, 161, 162, 163

Offset: 1

Paolo Xausa, Apr 01 2025

Conjecture: these are the numbers missing from A382621.

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

Cf. A347298, A382464, A382621, A382624 (complement).

A382623Q[k_] := MemberQ[Partition[IntegerDigits[k], 2, 1], {i_, j_?EvenQ} /; i <= j];
Select[Range[200], A382623Q]

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 "02468")
print([k for k in range(1, 164) if ok(k)]) # Michael S. Branicky, Apr 03 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

A382462 Lexicographically earliest sequence of distinct positive integers such that if a digit d in the digit stream (ignoring commas) is even, the previous digit is < d.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 31, 21, 23, 33, 34, 35, 36, 37, 38, 39, 51, 24, 53, 41, 25, 55, 56, 57, 58, 59, 71, 26, 73, 43, 45, 61, 27, 75, 63, 46, 77, 78, 79, 91, 28, 93, 47, 81, 29, 95, 65, 67, 83, 48, 97, 85, 68, 99, 111, 49, 112, 69

Offset: 1

Paolo Xausa, Mar 27 2025

Could be summarized as "even digit, previous smaller". A variant of A342042.

No term contains the digit 0. - Paolo Xausa, Apr 30 2025

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

Similar sequences: A342042, A342043, A342044, A342045, A382621, A382935, A383059.

Cf. A382463, A382464, A382465, A382466.

A382462list[nmax_] := Module[{a, s, invQ, fu = 2},
  invQ[k_] := invQ[k] = (If[#, s[k] = #]; #) & [MemberQ[Partition[IntegerDigits[k], 2, 1], {i_, j_?EvenQ} /; i >= j]];
  s[_] := False; s[1] = True;
  NestList[(a = fu; While[s[a] || invQ[a] || invQ[# + First[IntegerDigits[a]]], a++] & [Mod[#, 10]*10]; While[s[fu], fu++]; s[a] = True; a) &, 1, nmax-1]];
A382462list[100]

from itertools import count, islice
def cond(s):
    return all(s[i] > s[i-1] for i in range(1, len(s)) if s[i] in "02468")
def agen(): # generator of terms
    an, seen, s, m = 1, {1}, "1", 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 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

A383249 Positive integers ending with the digit 1, or containing an odd digit d immediately followed by a digit >= d.

Original entry on oeis.org

1, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 33, 34, 35, 36, 37, 38, 39, 41, 51, 55, 56, 57, 58, 59, 61, 71, 77, 78, 79, 81, 91, 99, 101, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135

Offset: 1

Paolo Xausa, Apr 26 2025

Conjecture: these are the numbers missing from A342045.

By way of disjointness and completeness, it is proved that this sequence is the complement of A342045. - Quinn Savitt, Apr 29 2025

Paolo Xausa, Table of n, a(n) for n = 1..10000
Quinn Savitt, Proof that A383249 is the complement of A342045

Cf. A342045, A383250 (complement).

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

A383249Q[k_] := Last[#] == 1 || MemberQ[Partition[#, 2, 1], {i_?OddQ, j_} /; j >= i] & [IntegerDigits[k]];
Select[Range[200], A383249Q]

def ok(n):
    if n%10 == 1: return True
    s = str(n)
    return 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(136) if ok(k)]) # 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

A382465 Positive integers such that every even digit except the first is immediately preceded by a smaller digit.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

A382623 Positive integers that contain an even digit d immediately preceded by a digit <= d.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

A382462 Lexicographically earliest sequence of distinct positive integers such that if a digit d in the digit stream (ignoring commas) is even, the previous digit is < d.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Python

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

A383249 Positive integers ending with the digit 1, or containing an odd digit d immediately followed by a digit >= d.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python