A288528 Numbers with consecutive positive decimal digits after the digits are sorted.

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, 132, 213, 231, 234, 243, 312, 321, 324, 342, 345, 354, 423, 432, 435, 453, 456, 465, 534, 543, 546, 564, 567, 576, 645, 654, 657, 675, 678, 687, 756, 765, 768, 786, 789, 798, 867, 876, 879, 897, 978, 987

Offset: 1

Author

Omar E. Pol, Jun 15 2017

Keywords

• nonn
• base
• easy
• fini

Comments

The last term is a(462331) = 987654321.

Observation: the number of terms mentioned above is also A014145(9). Also the sum of the 9th row in the triangle A288777.

It appears that the number of terms with k digits in this sequence is also A288777(9,k), k>=1.

Links

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

Crossrefs

Subsequence of A215014.

Supersequence of A138141.

Cf. A014145, A033075, A288777.

Programs

Python

def ok(n): return "".join(sorted(str(n))) in "123456789"
print([k for k in range(999) if ok(k)]) # Michael S. Branicky, Aug 04 2022

Python

# alternate for generating full sequence instantly
from itertools import permutations
frags = ["123456789"[i:j] for i in range(9) for j in range(i+1, 10)]
afull = sorted(int("".join(s)) for f in frags for s in permutations(f))
print(afull[:70]) # Michael S. Branicky, Aug 04 2022