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
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
KEYWORD
base,easy,nonn
AUTHOR
Rick L. Shepherd, Aug 29 2004
STATUS
approved