

A098155


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


2



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
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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



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



STATUS

approved



