A060857 Describe all the numbers already used (sorted into increasing order - not splitting numbers up into their digits).
1, 11, 31, 4113, 612314, 8112332416, 1113253342618, 131528344153628111, 1617210364354648211113, 181921239445661758110311213116, 2211121431146586276829210411112313216118
Offset: 0
Examples
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.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 0..60
- Onno M. Cain and Sela T. Enin, Inventory Loops (i.e. Counting Sequences) have Pre-period 2 max S_1 + 60, arXiv:2004.00209 [math.NT], 2020.
Crossrefs
Programs
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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 -
Mathematica
FromDigits /@ Nest[Append[#, Flatten@ Map[Reverse, Tally@ Sort@ Flatten@ # ] ] &, {{1}}, 10] (* Michael De Vlieger, Jul 15 2020 *) -
Python
def summarize_lst(lst): ans = [] for d in sorted(set(lst)): ans += [lst.count(d), d] return ans def aupton(nn): alst, arunninglst = [1], [1] for n in range(nn): nxt_lst = summarize_lst(arunninglst) arunninglst += nxt_lst alst.append(int("".join(map(str, nxt_lst)))) return alst print(aupton(10)) # Michael S. Branicky, Jan 11 2021
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