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A060857
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Describe all the numbers already used (sorted into increasing order - not splitting numbers up into their digits).
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15
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1, 11, 31, 4113, 612314, 8112332416, 1113253342618, 131528344153628111, 1617210364354648211113, 181921239445661758110311213116, 2211121431146586276829210411112313216118
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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FromDigits /@ Nest[Append[#, Flatten@ Map[Reverse, Tally@ Sort@ Flatten@ # ] ] &, {{1}}, 10] (* Michael De Vlieger, Jul 15 2020 *)
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PROG
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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
(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
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CROSSREFS
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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.
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KEYWORD
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base,nice,nonn
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AUTHOR
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STATUS
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approved
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