A377948 Numbers that have at least 1 repeated decimal digit and whose decimal digits are nondecreasing as place value decreases.

11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 112, 113, 114, 115, 116, 117, 118, 119, 122, 133, 144, 155, 166, 177, 188, 199, 222, 223, 224, 225, 226, 227, 228, 229, 233, 244, 255, 266, 277, 288, 299, 333, 334, 335, 336, 337, 338, 339, 344, 355, 366, 377, 388, 399

Offset: 1

Author

Michael De Vlieger, Nov 14 2024

Keywords

• nonn
• base
• easy

Comments

Intersection of A009994 and A109303.

Does not intersect either A009993 or A009995.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10938 (includes all numbers up to 7 digits long)

Crossrefs

Cf. A009993, A009994, A009995, A109303, A178788.

Programs

Mathematica

Select[Range[10^6], And[CountDistinct[#] != Length[#], AllTrue[Differences[#], # >= 0 &]] &[IntegerDigits[#]] &]
(* More efficient program: *)
b = 10; mm = b - 1; nn = 14;
s = Table[Map[Position[#, 1][[All, 1]] &,
  Permutations@ Join[ConstantArray[1, r], ConstantArray[0, mm - r] ] ],
    {r, Min[mm, nn]}];
Union@ Flatten@ Table[
  w = Apply[Join, Permutations /@ IntegerPartitions[n, Min[mm, n - 1] ] ];
  Reap[Do[
    Sow[Table[FromDigits[Flatten@
      MapIndexed[ConstantArray[m[[First[#2] ]], #1] &,
      w[[i]]], b], {m, s[[Length[w[[i]]] ]]} ] ],
    {i, Length[w]}] ][[-1, 1]], {n, 2, nn}]

Formula

A178788(a(n)) = 0.