A082927 -id:A082927 - cp's OEIS frontend

A098953 Slowest increasing sequence where each number is such that at least one pair of adjacent digits are consecutive, the first of the pair being the smaller.

12, 23, 34, 45, 56, 67, 78, 89, 101, 112, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 134, 145, 156, 167, 178, 189, 201, 212, 223, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 245, 256, 267, 278, 289, 301, 312, 323, 334, 340, 341, 342, 343, 344, 345

Offset: 1

Eric Angelini, Oct 21 2004

Corrected by Zak Seidov, Apr 15 2007

Michael S. Branicky, Table of n, a(n) for n = 1..10000

A similar sequence: A082927

from itertools import count, islice
def cond(n):
    d = list(map(int, str(n)))
    return any(d[i+1] == d[i]+1 for i in range(len(d)-1))
def agen():
    yield from filter(cond, count(1))
print(list(islice(agen(), 54))) # Michael S. Branicky, Dec 23 2021

a(51) and beyond from Michael S. Branicky, Dec 23 2021

A352927 Numbers whose digits are nonzero, consecutive, and all increasing or all decreasing.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 21, 23, 32, 34, 43, 45, 54, 56, 65, 67, 76, 78, 87, 89, 98, 123, 234, 321, 345, 432, 456, 543, 567, 654, 678, 765, 789, 876, 987, 1234, 2345, 3456, 4321, 4567, 5432, 5678, 6543, 6789, 7654, 8765, 9876, 12345, 23456, 34567, 45678, 54321, 56789, 65432, 76543, 87654, 98765, 123456, 234567, 345678

Offset: 1

N. J. A. Sloane, May 01 2022, following a suggestion from Ralph Sieber

There are 81 terms, corresponding to numbers that start with i and end with j, for 1 <= i <= 9, 1 <= j <= 9. - Michael S. Branicky, May 01 2022

Michael S. Branicky, Table of n, a(n) for n = 1..81

Cf. A033075, A082927, A138141, A215014.

Join[Range[9],Select[Range[350000],DigitCount[#,10,0]==0&&(Union[Differences[IntegerDigits[ #]]]=={1}||Union[Differences[IntegerDigits[#]]]=={-1})&]] (* Harvey P. Dale, Aug 13 2023 *)

def sgn(n): return 1 if n >= 0 else -1
def afull(): return sorted(int("".join(map(str, range(i, j+sgn(j-i), sgn(j-i))))) for i in range(1, 10) for j in range(1, 10))
print(afull()) # Michael S. Branicky, May 01 2022

A358054 Starting with 0, smallest integer not yet in the sequence such that no two neighboring digits differ by 1.

Original entry on oeis.org

0, 2, 4, 1, 3, 5, 7, 9, 6, 8, 11, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 64, 66, 68, 69, 70, 71, 72, 73, 74, 75, 77, 79, 90, 80

Offset: 0

Gavin Lupo and Eric Angelini, Oct 28 2022

Integers such as 10, 12, 21, 76, 6792, and 10744 (see A082927) will not appear in the sequence as they contain adjacent digits that differ by 1. Some integers may be disallowed only temporarily; for example, if a(n) = 79, and all nonnegative integers < 79 are already in the sequence, then a(n+1) = 90, because a(n+1) must not start with an 8, as it would differ by 1 from the digit "9" in 79. Now, a(n+2) can equal 80.

			a(0) = 0.
a(1) = 2. Cannot be 1. Smallest integer that can be placed = 2.
a(2) = 4. Cannot be 1 or 3. Smallest integer that can be placed = 4.
a(3) = 1. Cannot be 3 or 5. Smallest integer that can be placed = 1.
...
(Nonnegative integers < 86, disregarding invalid integers, have already appeared.)
a(74) = 86.
a(75) = 88. Cannot be 87, as it contains adjacent digits that differ by 1. Smallest integer that can be placed = 88.
a(76) = 111. Cannot be 89, 90->99 (9 and 8 differ by 1), or 100->110 (1 and 0 are adjacent and differ by 1). Smallest integer that can be placed = 111.

Gavin Lupo, Table of n, a(n) for n = 0..5000
David A. Corneth, PARI program

Cf. A082927, A219250.

\\ See PARI link \\ David A. Corneth, Oct 31 2022

A098954 Slowest increasing sequence where each number is such that at least one pair of adjacent digits are consecutive, the second one being the smallest.

Original entry on oeis.org

10, 21, 32, 43, 54, 65, 76, 87, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 121, 132, 143, 154, 165, 176, 187, 198, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 221, 232, 243, 254, 265, 276, 287, 298, 310, 320, 321, 322, 323, 324, 325, 326

Offset: 1

Eric Angelini, Oct 21 2004

			132 shows 32 and thus belongs to the sequence; 123 doesn't fit because the smallest digit (2) has to come in second.

Close to this sequence: A082927

cp's OEIS Frontend

A098953 Slowest increasing sequence where each number is such that at least one pair of adjacent digits are consecutive, the first of the pair being the smaller.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Python

Extensions

A352927 Numbers whose digits are nonzero, consecutive, and all increasing or all decreasing.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

A358054 Starting with 0, smallest integer not yet in the sequence such that no two neighboring digits differ by 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

A098954 Slowest increasing sequence where each number is such that at least one pair of adjacent digits are consecutive, the second one being the smallest.

Views

Author

Keywords

Examples

Crossrefs