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 A045918 Describe n. Also called the "Say What You See" or "Look and Say" sequence LS(n). 53
 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1110, 21, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 1210, 1211, 22, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 1310, 1311, 1312, 23, 1314, 1315, 1316, 1317, 1318, 1319, 1410, 1411, 1412, 1413, 24, 1415, 1416, 1417 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(1111111111) = a((10^10 - 1)/9) = 101 is the first term with an odd number of digits; 3-digit terms are unambiguous, but already the 2nd 4-digit term is LS( 12 ) = 1112 = LS( 2*(10^111-1)/9 ) ("hundred eleven 2's"). The smallest n such that LS(n) = LS(k) for some k < n (i.e. the largest n such that the restriction of LS to [0..n-1] is injective) appears to be 10*(10^11 - 1)/9 : LS(eleven '1's, one '0') = 11110 = LS(one '1', eleven '0's). - M. F. Hasler, Nov 14 2006 A121993 gives numbers m such that a(m) < m. - Reinhard Zumkeller, Jan 25 2014 REFERENCES J. H. Conway, The weird and wonderful chemistry of audioactive decay, in T. M. Cover and Gopinath, eds., Open Problems in Communication and Computation, Springer, NY 1987, pp. 173-188. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 Kevin Watkins, Abstract Interpretation Using Laziness: Proving Conway's Lost Cosmological Theorem, Kevin Watkins, Proving Conway's Lost Cosmological Theorem, POP seminar talk, CMU, Dec 2006 Eric Weisstein's World of Mathematics, Look and Say Sequence Wikipedia, Look-and-say sequence EXAMPLE 23 has "one 2, one 3", so a(23) = 1213. MAPLE LS:=n-> if n>9 then LS(op(convert(n, base, 10))) else for i from 2 to nargs do if args[i] <> n then RETURN(( LS( args[i..nargs] )*10^length(i-1) + i-1)*10 + n ) fi od: 10*nargs + n fi; # M. F. Hasler, Nov 14 2006 MATHEMATICA LookAndSayA[n_] := FromDigits@ Flatten@ IntegerDigits@ Flatten[ Through[{Length, First}[#]] & /@ Split@ IntegerDigits@ n] (* Robert G. Wilson v, Jan 27 2012 *) PROG (PARI) A045918(a)={my(c=1); for(j=2, #a=Vec(Str(a)), if(a[j-1]==a[j], a[j-1]=""; c++, a[j-1]=Str(c, a[j-1]); c=1)); a[#a]=Str(c, a[#a]); eval(concat(a))} \\ M. F. Hasler, Jan 27 2012 (Haskell) see Watkins link, p. 3. import Data.List (unfoldr, group); import Data.Tuple (swap) a045918 0 = 10 a045918 n = foldl (\v d -> 10 * v + d) 0 \$ say \$ reverse \$ unfoldr (\x -> if x == 0 then Nothing else Just \$ swap \$ divMod x 10) n where say = concat . map code . group code xs = [toInteger \$ length xs, head xs] -- Reinhard Zumkeller, Aug 09 2012 (Python) from re import finditer def A045918(n): return int(''.join([str(len(m.group(0)))+m.group(0) for m in finditer(r'(\d)\1*', str(n))])) # Chai Wah Wu, Dec 03 2014 (Python) from itertools import groupby def LS(n): return int(''.join(str(len(list(g)))+k for k, g in groupby(str(n)))) print([LS(n) for n in range(48)]) # Michael S. Branicky, Jul 27 2022 CROSSREFS Cf. A005150. See also A056815. Sequence in context: A047842 A047843 A097598 * A244112 A088476 A248014 Adjacent sequences: A045915 A045916 A045917 * A045919 A045920 A045921 KEYWORD nonn,base AUTHOR N. J. A. Sloane EXTENSIONS Added Mma program from A056815. - N. J. A. Sloane, Feb 02 2012 STATUS approved

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Last modified June 9 13:19 EDT 2023. Contains 363180 sequences. (Running on oeis4.)