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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

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}], #[[1]] > 0 &]; Table[dc[n], {n, 0, 46}] (* Ray Chandler *)

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

N. J. A. Sloane

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 January 18 23:05 EST 2019. Contains 319282 sequences. (Running on oeis4.)