A366966 Numbers whose difference between the largest and smallest digits is equal to 9.

90, 109, 190, 209, 290, 309, 390, 409, 490, 509, 590, 609, 690, 709, 790, 809, 890, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 910, 920, 930, 940, 950, 960, 970, 980, 990, 1009, 1019, 1029, 1039, 1049, 1059, 1069, 1079, 1089, 1090, 1091, 1092, 1093, 1094, 1095

Offset: 1

Author

Stefano Spezia, Oct 30 2023

Keywords

• nonn
• base
• easy

Comments

The number of n-digit terms of this sequence is 9*10^(n-1) - 17*9^(n-1) + 8^n.

Crossrefs

Cf. A037904.

Cf. A010785 (difference = 0), A366958 (difference = 1), A366959 (difference = 2), A366960 (difference = 3), A366961 (difference = 4), A366962 (difference = 5), A366963 (difference = 6), A366964 (difference = 7), A366965 (difference = 8).

Programs

Mathematica

Select[Range[1095],Max[d=IntegerDigits[#]]-Min[d]==9 &]

PARI

isok(n) = my(d=digits(n)); vecmax(d) - vecmin(d) == 9; \\ Michel Marcus, Nov 05 2023

Python

def ok(n): return max(d:=list(map(int, str(n))))-min(d) == 9
print([k for k in range(1100) if ok(k)]) # Michael S. Branicky, Oct 30 2023

Python

from itertools import chain, count, islice, combinations_with_replacement
from sympy.utilities.iterables import multiset_permutations
def A366966_gen(): # generator of terms
    return chain.from_iterable(sorted(int(''.join(str(d) for d in t)) for c in combinations_with_replacement(range(10),l) for t in multiset_permutations((0,9)+c) if t[0]) for l in count(0))
A366966_list = list(islice(A366966_gen(),30)) # Chai Wah Wu, Nov 10 2023