

A060857


Describe all the numbers already used (sorted into increasing order  not splitting numbers up into their digits).


12



1, 11, 31, 4113, 612314, 8112332416, 1113253342618, 131528344153628111, 1617210364354648211113, 181921239445661758110311213116, 2211121431146586276829210411112313216118
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OFFSET

0,2


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..60
Onno M. Cain, Sela T. Enin, Inventory Loops (i.e. Counting Sequences) have Preperiod 2 max S_1 + 60, arXiv:2004.00209 [math.NT], 2020.


EXAMPLE

One; one one; three ones; four ones, one three; six ones, two threes, one four; eight ones, one two, three threes, two fours, one six; eleven ones, three twos, five threes, three fours, two sixes, one eight; thirteen [note not 15] ones, five twos, eight threes, four fours, one five, three sixes, two eights, one eleven [note than numbers >9 are preserved as wholes rather than as a collection of digits]; etc.


MATHEMATICA

FromDigits /@ Nest[Append[#, Flatten@ Map[Reverse, Tally@ Sort@ Flatten@ # ] ] &, {{1}}, 10] (* Michael De Vlieger, Jul 15 2020 *)


PROG

(Haskell)
import Data.List (group, sort, transpose)
a060857 n = a060857_list !! n
a060857_list = 1 : f [1] :: [Integer] where
f xs = (read $ concatMap show ys) : f (xs ++ ys) where
ys = concat $ transpose [map length zss, map head zss]
zss = group $ sort xs
 Reinhard Zumkeller, Jan 25 2014


CROSSREFS

This is a combination of methods used in A005151 and A045982. The first word of each term (the number of ones used earlier) seems to be equal to A030711 and A030761.
Sequence in context: A068839 A228530 A177360 * A045982 A059134 A215727
Adjacent sequences: A060854 A060855 A060856 * A060858 A060859 A060860


KEYWORD

base,nice,nonn


AUTHOR

Henry Bottomley, May 03 2001


STATUS

approved



