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

1,1

Comments

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

Links

Table of n, a(n) for n=1..51.

Mathematica

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

Prog

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

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).

Sequence in context: A045097 A074817 A333745 * A043224 A039401 A044004

Adjacent sequences: A366963 A366964 A366965 * A366967 A366968 A366969

Keyword

nonn,base,easy

Author

Stefano Spezia, Oct 30 2023

Status

approved