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

1,2

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

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 *)

Crossrefs

Sequence in context: A247700 A105776 A044354 * A044735 A247701 A039439

Adjacent sequences: A140054 A140055 A140056 * A140058 A140059 A140060

Keyword

base,easy,nonn

Author

Rick L. Shepherd, May 03 2008

Extensions

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

Status

approved