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

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

1,2

Comments

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

Links

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

Mathematica

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

Prog

(Python)
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

Crossrefs

Cf. A033075, A082927, A138141, A215014.

Sequence in context: A095160 A356350 A288528 * A200372 A059043 A259236

Adjacent sequences: A352924 A352925 A352926 * A352928 A352929 A352930

Keyword

nonn,base,fini,full

Author

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

Status

approved