A098155 Summarize the previous term in base 4 (in increasing order).

1, 11, 21, 1112, 3112, 211213, 312213, 212223, 1110213, 101011213, 201111213, 101112213, 101112213, 101112213, 101112213, 101112213, 101112213, 101112213, 101112213, 101112213, 101112213, 101112213, 101112213, 101112213, 101112213

Offset

1,2

Comments

Let a(1)=1. Describing a(1) as "one 1" again gives a(2)=11 (same digit string as A005151 and similar sequences). Likewise, a(3) through a(8) have the same digit strings as the corresponding terms of A005151, but describing a(8) as "one 1, four 2s, one 3" gives a(9)=1110213 when the frequency of digit occurrence is written in base 4 and followed by the digit counted.

Links

Table of n, a(n) for n=1..25.

Onno M. Cain, Sela T. Enin, Inventory Loops (i.e. Counting Sequences) have Pre-period 2 max S_1 + 60, arXiv:2004.00209 [math.NT], 2020.

Formula

a(n) = 101112213 for all n >= 12 (see example).

Example

Summarizing a(12) = 101112213 in increasing digit order, there are "one 0, five 1's, two 2s, one 3", so concatenating 1 0 11 1 2 2 1 3 gives a(13) = 101112213 (=a(14)=a(15)=...).

Mathematica

Nest[Append[#, FromDigits[Flatten@ Map[IntegerDigits[#, 4] & /@ Reverse@ # &, Tally@ Sort@ IntegerDigits@ #[[-1]] ] ]] &, {1}, 24] (* Michael De Vlieger, Jul 15 2020 *)

Crossrefs

Cf. A098153 (binary), A098154 (ternary), A005151 (decimal and digit strings for all other bases b >= 5).

Sequence in context: A138485 A006711 A005151 * A098154 A007890 A063850

Adjacent sequences: A098152 A098153 A098154 * A098156 A098157 A098158

Keyword

base,easy,nonn

Author

Rick L. Shepherd, Aug 29 2004

Status

approved