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 A047842 Describe n (count digits in order of increasing value, ignoring missing digits). 25
 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1011, 21, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 1012, 1112, 22, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 1013, 1113, 1213, 23, 1314, 1315, 1316, 1317, 1318, 1319, 1014, 1114, 1214, 1314, 24, 1415, 1416 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Digit count of n. The digit count numerically summarizes the frequency of digits 0 through 9 in that order when they occur in a number. - Lekraj Beedassy, Jan 11 2007 Numbers which are digital permutations of one another have the same digit count. Compare with first entries of "Look And Say " or LS sequence A045918. As in the latter, a(n) has first odd-numbered-digit entry occurring at n=1111111111 with digit count 101, but a(n) has first ambiguous term 1011. For digit count invariants, i.e., n such that a(n)=n, see A047841. - Lekraj Beedassy, Jan 11 2007 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 Onno M. Cain, Sela T. Enin, Inventory Loops (i.e. Counting Sequences) have Pre-period 2 max S_1 + 60, arXiv:2004.00209 [math.NT], 2020. Andre Kowacs, Studies on the Pea Pattern Sequence, arXiv:1708.06452 [math.HO], 2017. FORMULA a(a(n)) = A235775(n). a(A010785(n)) = A244112(A010785(n)). - Reinhard Zumkeller, Nov 11 2014 EXAMPLE a(31)=1113 because (one 1, one 3) make up 31. 101 contains one 0 and two 1's, so a(101)=1021. a(131)=2113. MATHEMATICA dc[n_] :=FromDigits@Flatten@Select[Table[{DigitCount[n, 10, k], k}, {k, 0, 9}], #[] > 0 &]; Table[dc[n], {n, 0, 46}] (* Ray Chandler, Jan 09 2009 *) Array[FromDigits@ Flatten@ Map[Reverse, Tally@ Sort@ IntegerDigits@ #] &, 46] (* Michael De Vlieger, Jul 15 2020 *) PROG (Haskell) import Data.List (sort, group); import Data.Function (on) a047842 :: Integer -> Integer a047842 n = read \$ concat \$    zipWith ((++) `on` show) (map length xs) (map head xs)    where xs = group \$ sort \$ map (read . return) \$ show n -- Reinhard Zumkeller, Jan 15 2014 (Python) def A047842(n):     s, x = '', str(n)     for i in range(10):         y = str(i)         c = str(x.count(y))         if c != '0':             s += c+y     return int(s) # Chai Wah Wu, Jan 03 2015 (PARI) A047842(n, c=1, S="")={for(i=2, #n=vecsort(digits(n)), n[i]==n[i-1]&&c++&&next; S=Str(S, c, n[i-1]); c=1); eval(Str(S, c, if(n, n[#n])))} \\ M. F. Hasler, Feb 25 2018 CROSSREFS Cf. A005151, A047841, A047843, A127354, A127355. Cf. A235775. Cf. A244112 (the same but in order of decreasing value of digits), A010785. Cf. A005150 (Look and Say: describe the number digit-wise instead of overall count) Sequence in context: A102236 A250040 A321485 * A047843 A097598 A045918 Adjacent sequences:  A047839 A047840 A047841 * A047843 A047844 A047845 KEYWORD nonn,easy,base,nice AUTHOR EXTENSIONS Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar STATUS approved

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Last modified October 23 07:27 EDT 2020. Contains 337964 sequences. (Running on oeis4.)