A366958 Numbers whose difference between the largest and smallest digits is equal to 1.

10, 12, 21, 23, 32, 34, 43, 45, 54, 56, 65, 67, 76, 78, 87, 89, 98, 100, 101, 110, 112, 121, 122, 211, 212, 221, 223, 232, 233, 322, 323, 332, 334, 343, 344, 433, 434, 443, 445, 454, 455, 544, 545, 554, 556, 565, 566, 655, 656, 665, 667, 676, 677, 766, 767, 776, 778, 787, 788

Offset: 1

Author

Stefano Spezia, Oct 30 2023

Keywords

• nonn
• base
• easy

Comments

The number of n-digit terms of this sequence is 17*A000225(n-1).

Crossrefs

Cf. A000225, A037904.

Cf. A010785 (difference = 0), A366959 (difference = 2), A366960 (difference = 3), A366961 (difference = 4), A366962 (difference = 5), A366963 (difference = 6), A366964 (difference = 7), A366965 (difference = 8), A366966 (difference = 9).

Programs

Mathematica

Select[Range[800],Max[d=IntegerDigits[#]]-Min[d]==1 &]

PARI

isok(n) = my(d=digits(n)); vecmax(d) - vecmin(d) == 1; \\ Michel Marcus, Oct 30 2023

Python

def ok(n): return max(d:=list(map(int, str(n))))-min(d) == 1
print([k for k in range(800) if ok(k)]) # Michael S. Branicky, Oct 30 2023

Python

# faster version for large terms
from itertools import count, islice, product
def agen(diff=1): # generator of terms; change diff for A366960-A366966
    for digits in count(2):
        s = set()
        for lo in range(10-diff):
            hi = lo + diff
            allowed = list(range(lo, hi+1))
            for p in product(allowed, repeat=digits):
                if p[0]==0 or lo not in p or hi not in p: continue
                s.add(int("".join(map(str, p))))
        yield from sorted(s)
print(list(islice(agen(), 60))) # Michael S. Branicky, Oct 30 2023