A366959 Numbers whose difference between the largest and smallest digits is equal to 2.

13, 20, 24, 31, 35, 42, 46, 53, 57, 64, 68, 75, 79, 86, 97, 102, 113, 120, 123, 131, 132, 133, 200, 201, 202, 210, 213, 220, 224, 231, 234, 242, 243, 244, 311, 312, 313, 321, 324, 331, 335, 342, 345, 353, 354, 355, 422, 423, 424, 432, 435, 442, 446, 453, 456, 464, 465, 466

Offset

1,1

Comments

The number of n-digit terms of this sequence is (46*3^n - 93*2^n + 48)/6.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

F:= proc(d) local L, i;
   L:= select(t -> max(t) = 2 and min(t) = 0, map(convert, [$3^d..2*3^d-1], base, 3));
   L:= map(t -> add(t[-i-1]*10^(i-1), i=1..nops(t)-1), L);
   L:= map(t -> seq(t+i*(10^d-1)/9, i=0..7), L);
   op(sort(select(t -> t >= 10^(d-1), L)));
end proc:
F(2), F(3), F(4); # Robert Israel, Nov 10 2023

Mathematica

Select[Range[500], Max[d=IntegerDigits[#]]-Min[d]==2 &]

Prog

(Python)
def ok(n): return max(d:=list(map(int, str(n))))-min(d) == 2
print([k for k in range(500) 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 A366959_gen(): # generator of terms
    return chain.from_iterable(sorted(int(''.join(str(d) for d in t)) for a in range(8) for c in combinations_with_replacement(range(a, a+3), l) for t in multiset_permutations((a, a+2)+c) if t[0]) for l in count(0))
A366959_list = list(islice(A366959_gen(), 30)) # Chai Wah Wu, Nov 10 2023
(PARI) isok(n) = my(d=digits(n)); vecmax(d) - vecmin(d) == 2; \\ Michel Marcus, Nov 05 2023

Crossrefs

Cf. A037904.

Cf. A010785 (difference = 0), A366958 (difference = 1), A366960 (difference = 3), A366961 (difference = 4), A366962 (difference = 5), A366963 (difference = 6), A366964 (difference = 7), A366965 (difference = 8), A366966 (difference = 9).

Sequence in context: A095040 A069195 A185126 * A098956 A302390 A014158

Adjacent sequences: A366956 A366957 A366958 * A366960 A366961 A366962

Keyword

nonn,base,easy

Author

Stefano Spezia, Oct 30 2023

Status

approved