A140057 Numbers such that each decimal digit d (for all d in the range 1 <= d <= 9) occurs only in runs of length exactly d.

1, 22, 122, 221, 333, 1221, 1333, 3331, 4444, 13331, 14444, 22122, 22333, 33322, 44441, 55555, 122122, 122333, 133322, 144441, 155555, 221221, 221333, 223331, 224444, 333122, 333221, 444422, 555551, 666666, 1221221, 1221333, 1223331

Offset: 1

Author

Rick L. Shepherd, May 03 2008

Keywords

• base
• easy
• nonn

Comments

Number of terms less than 10^k: 1, 2, 5, 9, 16, 30, 53, 92, 163, 286, 497, 869, 1516, 2639, 4606, 8032, 13993, ..., . - Robert G. Wilson v

Number of terms of k digits: 1, 1, 3, 4, 7, 14, 23, 39, 71, 123, 211, 372, 647, 1123, 1967, 3426, 5961, ..., ; not the same as A003242. - Robert G. Wilson v

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..8032

Programs

Mathematica

(* first do *) Needs["Combinatorica`"] (* then *) f[n_] := Block[{ pa=Partitions@ n, len = PartitionsP@ n, s, lst, lmt}, s = Select[Range@len, pa[[ #, 1]] < 10 &]; lst=Take[pa, {s[[1]], -1}]; lst = Flatten[ DistinctPermutations /@ lst, 1]; lmt = Length@ lst; While[lmt != 0, If[ Split[lst[[lmt]]] != Partition[lst[[lmt]], 1], lst = Delete[lst, lmt]]; lmt-- ]; Sort@ (FromDigits /@ Flatten /@ (lst /. {x_Integer -> Table[x, {x}]}))] (* Robert G. Wilson v, May 25 2008 *)
Select[Range[1250000],AllTrue[Split[IntegerDigits[#]],Length[#] == #[[1]]&]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 04 2019 *)

Extensions

Definition expanded by N. J. A. Sloane, May 20 2008