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

1,2

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

Prog

(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

Crossrefs

Subsequence of A215014.

Supersequence of A138141.

Cf. A014145, A033075, A288777.

Sequence in context: A308561 A095160 A356350 * A352927 A200372 A059043

Adjacent sequences: A288525 A288526 A288527 * A288529 A288530 A288531

Keyword

nonn,base,easy,fini

Author

Omar E. Pol, Jun 15 2017

Status

approved