A210666 Numbers with at least three digits in which all digits but one are the same.

100, 101, 110, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 131, 133, 141, 144, 151, 155, 161, 166, 171, 177, 181, 188, 191, 199, 200, 202, 211, 212, 220, 221, 223, 224, 225, 226, 227, 228, 229, 232, 233, 242, 244, 252, 255, 262, 266, 272, 277, 282, 288

Offset: 1

Author

Arkadiusz Wesolowski, May 08 2012

Keywords

• base
• easy
• nonn
• less

Comments

Each k-digit term has k-1 appearances of a digit, d1, and 1 appearance of a different digit, d2, and k-1 >= 2 so that d1 is repeated. Specifically, the 2-digit terms of A010784 are not terms here. - Michael S. Branicky, May 22 2022

a(n) = A031955(n+81) for n <= 244.

For n <= 243, i.e., the 3-digit terms, a(n) = A218556(n+10). - M. F. Hasler, Nov 02 2012

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A031955. Supersequence of A164937.

Cf. A010784, A031955, A218556.

Programs

Mathematica

lst = {}; Do[If[SortBy[Tally[IntegerDigits[n]], Last][[-1, -1]] == IntegerLength[n] - 1, AppendTo[lst, n]], {n, 100, 288}]; lst
lst = {}; Do[r = Table[a, {n}]; Do[c = FromDigits@Permutations[Join[{d}, r]]; If[d == 0, c = Rest[c]]; AppendTo[lst, c], {d, 0, 9}], {a, 0, 9}, {n, 2, 2}]; Drop[Union@Flatten[lst], 19]
nrepQ[n_] := Module[{dg = Select[DigitCount[n], # > 0 &]}, Length[dg] == 2 && Min[dg] == 1 && Max[dg] > 1]; Select[Range[300], nrepQ] (* Harvey P. Dale, Nov 20 2012 *)

Python

from itertools import count, islice
def agen(): # generator of terms
    for d in count(3):
        dterms = set()
        for most in "123456789":
            dterms.add(int(most + "0"*(d-1)))
            for diff in "0123456789":
                if most == diff: continue
                cands = (most*i + diff + most*(d-1-i) for i in range(d))
                dterms.update(int(t) for t in cands if t[0] != "0")
        yield from sorted(dterms)
print(list(islice(agen(), 52))) # Michael S. Branicky, May 17 2022