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

1,1

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

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 *)

Prog

(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

Crossrefs

Subsequence of A031955. Supersequence of A164937.

Cf. A010784, A031955, A218556.

Sequence in context: A090429 A248711 A079112 * A280825 A233345 A091254

Adjacent sequences: A210663 A210664 A210665 * A210667 A210668 A210669

Keyword

base,easy,nonn,less

Author

Arkadiusz Wesolowski, May 08 2012

Status

approved