A193582 -id:A193582 - cp's OEIS frontend

A004185 Arrange digits of n in increasing order, then (for n > 0) omit the zeros.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2, 12, 22, 23, 24, 25, 26, 27, 28, 29, 3, 13, 23, 33, 34, 35, 36, 37, 38, 39, 4, 14, 24, 34, 44, 45, 46, 47, 48, 49, 5, 15, 25, 35, 45, 55, 56, 57, 58, 59, 6, 16, 26, 36, 46, 56, 66, 67, 68, 69, 7, 17, 27, 37, 47

Offset: 0

N. J. A. Sloane

Record values: A009994. - Reinhard Zumkeller, Dec 05 2009
If we define "sortable primes" as prime numbers that remain prime when their digits are sorted in increasing order, then all absolute primes (A003459) are sortable primes but not all sortable primes are absolute primes. For example, 311 is both sortable and absolute, and 271 is sortable but not absolute, since its digits can be permuted to 217 = 7 * 31 or 712 = 2^3 * 89, etc. - Alonso del Arte, Oct 05 2013
The above mentioned "sortable primes" are listed in A211654, the nontrivial ones (with digits not in nondecreasing order) in A086042. - M. F. Hasler, Jul 30 2019

			a(19) = 19 because the digits are already in increasing order.
a(20) = 2 because the digits of 20 are 2 and 0, which in increasing order are 0 and 2, but since zero-padding is not allowed on the left, the zero digit is dropped and we are left with 2.
a(21) = 12 because the digits of 21 are 2 and 1, which in increasing order are 1 and 2.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A004719, A004151, A004086, A004186, A009996, A221714, A073138, A193581, A193582, A065641.

Cf. A211654 (sortable primes) and subsequence A086042 (nontrivial solutions).

import Data.List (sort)
a004185 n = read $ sort $ show n :: Integer
-- Reinhard Zumkeller, Aug 10 2011

A004185:=func; [n eq 0 select 0 else A004185(n): n in [0..57]]; // Bruno Berselli, Apr 03 2012

A004185 := proc(n)
    local dgs;
    convert(n,base,10) ;
    dgs := sort(%,`>`) ;
    add( op(i,dgs)*10^(i-1),i=1..nops(dgs)) ;
end proc:
seq(A004185(n),n=0..20) ; # R. J. Mathar, Jul 26 2015

FromDigits[Sort[DeleteCases[IntegerDigits[#], 0]]]&/@Range[0, 60] (* Harvey P. Dale, Nov 29 2011 *)

a(n)=fromdigits(vecsort(digits(n))) \\ Charles R Greathouse IV, Feb 06 2017

def A004185(n):
    return int(''.join(sorted(str(n))).replace('0','')) if n > 0 else 0 # Chai Wah Wu, Nov 10 2015

A065641 Smallest number with persistence n for the sort-and-subtract-sequence.

Original entry on oeis.org

0, 1, 10, 60, 90, 101, 120, 380, 450, 505, 807, 1020, 1070, 1303, 1450, 3810, 10020, 10404, 10560, 16056, 16200, 18088, 20322, 20580, 35790, 79000, 80088, 90877, 243700, 279509, 330832, 374330, 380038, 903655, 1002404, 1005064, 1020828

Offset: 0

Ulrich Schimke (ulrschimke(AT)aol.com), Dec 03 2001

Sort the digits of an integer and subtract the result from the original. Continue with the result until you reach 0. The sequence gives the least integer that needs n steps to reach 0.

			60 is the smallest number that needs 3 steps to reach 0: 60 -> 60 - 06 = 54 -> 54 - 45 = 9 -> 9 - 9 = 0, hence a(3) = 60.

David W. Wilson and Reinhard Zumkeller, Table of n, a(n) for n = 0..100 (a(n) for n = 1..55 from Reinhard Zumkeller).

Cf. A004185, A193582.

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a065641 n = a065641_list !! (n-1)
a065641_list = map (fromJust . (`elemIndex` a193582_list)) [1..]
-- Reinhard Zumkeller,Aug 10 2011

Persist[n_] := Length[NestWhileList[# - FromDigits[Sort[IntegerDigits[#]]] &, n, # != 0 &]] - 1; nn = 20; t = Table[0, {nn}]; cnt = 0; k = 0; While[cnt < nn, k++; c = Persist[k]; If[c <= nn && t[[c]] == 0, t[[c]] = k; cnt++]]; t  (* Harvey P. Dale, Mar 24 2011 *)
persist[n_]:=Length[NestWhileList[#-FromDigits[Sort[IntegerDigits[#]]]&,n,#!=0&]]-1; Module[ {nn=103*10^4,tbl},tbl=Table[{n,persist[n]},{n,0,nn}];DeleteDuplicates[ tbl,GreaterEqual[ #1[[2]],#2[[2]]]&]][[;;,1]] (* Harvey P. Dale, Sep 03 2023 *)

Added a(0) = 0. David W. Wilson, Jan 08 2017

A343639 a(n) = (Sum of digits of 9*n) / 9.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 0

M. F. Hasler, May 19 2021

Similar to, but different from A193582, A326307, ...

Consider g = A008585 = multiply by 3, and its left inverse h = A002264, h o g = id (but g o h = id only on (the range of) A008585). In the spirit of group theory, we can write ad(g) = (x -> h o x o g), then A343638 = ad(A008585)(A007953) and this A343639 = ad(A008585)(A343638) = ad(A008585)^2 (A007953).

Cf. A007953 (digit sum), A008591 (9n), A343638 (similar for 3), A083824 (9*n reversed and divided by 9), A279777 (a(n)=3).

a[n_] := Plus @@ IntegerDigits[9*n]/9; Array[a, 100, 0] (* Amiram Eldar, May 19 2021 *)

PARI
```
A343639(n)=sumdigits(9*n)/9
```

a(n) = A007953(A008591(n))/9, by definition. - Felix Fröhlich, May 19 2021

a(n) = A343638(3*n)/3 = A002264(A343638(A008585(n))), i.e., A343639 = A002264 o A343638 o A008585 (just as A343638 = A002264 o A007953 o A008585).

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A004185 Arrange digits of n in increasing order, then (for n > 0) omit the zeros.

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A065641 Smallest number with persistence n for the sort-and-subtract-sequence.

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A343639 a(n) = (Sum of digits of 9*n) / 9.

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