A004185 -id:A004185 - cp's OEIS frontend

A036839 RATS(n): Reverse Add Then Sort the digits.

0, 2, 4, 6, 8, 1, 12, 14, 16, 18, 11, 22, 33, 44, 55, 66, 77, 88, 99, 11, 22, 33, 44, 55, 66, 77, 88, 99, 11, 112, 33, 44, 55, 66, 77, 88, 99, 11, 112, 123, 44, 55, 66, 77, 88, 99, 11, 112, 123, 134, 55, 66, 77, 88, 99, 11, 112, 123, 134, 145, 66, 77

Offset: 0

N. J. A. Sloane, Jan 19 2002

a(n) = RATS(n), not RATS(a(n-1)).

Row 10 of A288535. - Andrey Zabolotskiy, Jun 14 2017

			1 -> 1 + 1 = 2, so a(1) = 2; 3 -> 3 + 3 = 6, so a(3) = 6.

Indranil Ghosh, Table of n, a(n) for n = 0..50000 (terms 0..1000 from T. D. Noe)
R. K. Guy, Conway's RATS and other reversals, Unsolved Problems Column, American Math. Monthly, Vol. 96, pp. 425-428, May 1989.
Eric Weisstein's World of Mathematics, RATS Sequence

Cf. A004000, A004185, A288535.

Cf. A161593, A114611, A009994, A004086.

a036839 = a004185 . a056964  -- Reinhard Zumkeller, Mar 14 2012

read transforms; RATS := n -> digsort(n + digrev(n));

FromDigits[Sort[IntegerDigits[#+FromDigits[Reverse [IntegerDigits[#]]]]]] & /@Range[0,80]  (* Harvey P. Dale, Mar 26 2011 *)

def A036839(n):
    x = str(n+int(str(n)[::-1]))
    return int("".join(sorted(x))) # Indranil Ghosh, Jan 28 2017

Form m by Reversing the digits of n, Add m to n Then Sort the digits of the sum into increasing order to get a(n).

a(n) = A004185(A056964(n)). [Reinhard Zumkeller, Mar 14 2012]

A033860 Sort-then-add sequence: a(n+1) = a(n) + sort(a(n)).

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 55, 110, 121, 233, 466, 932, 1171, 2288, 4576, 9143, 10492, 11741, 22888, 45776, 91453, 104912, 116161, 227327, 449704, 494183, 628672, 855350, 890908, 899807, 978706, 1046495, 1191064, 1302533, 1425868, 2671556, 3927223, 6150602, 6163168

Offset: 1

David W. Wilson

			After 9143 the next term is 9143 + 1349 = 10492.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A070196, A004185.

a033860 n = a033860_list !! (n-1)
a033860_list = iterate a070196 1
-- Reinhard Zumkeller, Apr 03 2015

a:= proc(n) option remember; `if`(n=1, 1, (t->
      t+parse(cat(sort(convert(t, base, 10))[])))(a(n-1)))
    end:
seq(a(n), n=1..40);  # Alois P. Heinz, Jan 15 2024

NestList[#+FromDigits[Sort[IntegerDigits[#]]]&,1,40] (* Harvey P. Dale, Jul 24 2016 *)

from itertools import islice
def agen(an=1): # generator of terms
    while True: yield an; an = an + int("".join(sorted(str(an))))
print(list(islice(agen(), 100))) # Michael S. Branicky, Jan 15 2024

a(n+1) = A070196(a(n)). - Reinhard Zumkeller, Apr 03 2015

A070196 a(n) = n plus the sorted version of the base-10 digits of n.

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 11, 22, 24, 26, 28, 30, 32, 34, 36, 38, 22, 33, 44, 46, 48, 50, 52, 54, 56, 58, 33, 44, 55, 66, 68, 70, 72, 74, 76, 78, 44, 55, 66, 77, 88, 90, 92, 94, 96, 98, 55, 66, 77, 88, 99, 110, 112, 114, 116, 118, 66, 77, 88, 99, 110, 121, 132, 134

Offset: 0

Eric W. Weisstein, Apr 27 2002

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Sort-Then-Add Sequence

Cf. A033862.

Cf. A004185, A033860 (iterated, starting with 1).

a070196 n = n + a004185 n  -- Reinhard Zumkeller, Apr 03 2015

a:= n-> n+parse(cat(sort(convert(n, base, 10))[])):
seq(a(n), n=0..67);  # Alois P. Heinz, Jan 15 2024

Table[n+FromDigits[Sort[IntegerDigits[n]]],{n,0,70}] (* Harvey P. Dale, Feb 08 2020 *)

def a(n): return n + int("".join(sorted(str(n))))
print([a(n) for n in range(68)]) # Michael S. Branicky, Jan 15 2024

a(n) = n + A004185(n). - Reinhard Zumkeller, Apr 03 2015

Zero prepended and offset changed by Reinhard Zumkeller, Apr 03 2015

A069638 "Sorted" sum of two previous terms, beginning with 0,1. "Sorted" means to sort the digits of the sum in ascending order.

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 13, 12, 25, 37, 26, 36, 26, 26, 25, 15, 4, 19, 23, 24, 47, 17, 46, 36, 28, 46, 47, 39, 68, 17, 58, 57, 115, 127, 224, 135, 359, 449, 88, 357, 445, 28, 347, 357, 47, 44, 19, 36, 55, 19, 47, 66, 113, 179, 229, 48, 277, 235, 125, 36, 116, 125, 124, 249, 337

Offset: 0

Gil Broussard, Jan 16 2004

The maximum value in this sequence is 667. After the 75th term, the next 120 terms (a(76) - a(195)) repeat as a group infinitely.

			a(8)=12 because a(7)+a(6)=13+8=21 and the digits of 21 sorted in ascending order = 12.
Also a(17)=4 because a(16)+a(15)=15+25=40 and the digits of 40 sorted in ascending order = 04, or just 4;

Zak Seidov, Table of n, a(n) for n = 0..1000

Cf. A000045, A001129, A004185, A237575, A237671.

a:= proc(n) option remember; `if`(n<2, n, parse(cat(
      sort(convert(a(n-1)+a(n-2), base, 10))[])))
    end:
seq(a(n), n=0..77);  # Alois P. Heinz, Aug 31 2022

a[0]:=0
a[1]:=1
a[n_] := a[n]=FromDigits[Sort[IntegerDigits[a[n-1]+a[n-2]]]] (* Peter J. C. Moses, Feb 08 2014 *)
nxt[{a_,b_}]:={b,FromDigits[Sort[IntegerDigits[a+b]]]}; NestList[nxt,{0,1},70][[All,1]] (* Harvey P. Dale, Jul 27 2020 *)

a, terms = [0, 1], 66
[a.append(int("".join(sorted(str(a[-2]+a[-1]))))) for n in range(2, terms)]
print(a) # Michael S. Branicky, Aug 31 2022

a(n) = SORT[a(n-1) + a(n-2)].

A321540 3^n with digits rearranged into nondecreasing order.

Original entry on oeis.org

1, 3, 9, 27, 18, 234, 279, 1278, 1566, 13689, 4599, 114777, 113445, 1233459, 2467899, 1344789, 1234467, 11123469, 23447889, 1112246667, 134446788, 12333456, 113356899, 11234477889, 122234456889, 23444678889, 1222345568889, 2445567778899

Offset: 0

N. J. A. Sloane, Nov 19 2018

The following are parallel families: A000079 (2^n), A004094 (2^n reversed), A028909 (2^n sorted up), A028910 (2^n sorted down), A036447 (double and reverse), A057615 (double and sort up), A263451 (double and sort down); A000244 (3^n), A004167 (3^n reversed), A321540 (3^n sorted up), A321539 (3^n sorted down), A163632 (triple and reverse), A321542 (triple and sort up), A321541 (triple and sort down).

Cf. A004185.

[Seqint(Reverse(Sort(Intseq(3^n)))):n in [0..35]]; // Vincenzo Librandi, Jan 22 2020

Table[FromDigits[Sort[IntegerDigits[3^n]]], {n, 0, 40}] (* Vincenzo Librandi, Jan 22 2020 *)

def A321540(n): return int(''.join(sorted(str(3**n)))) # Chai Wah Wu, Nov 10 2022

a(n) = A004185(A000244(n)). - Michel Marcus, Nov 10 2022

A052008 a(n) = 'n with digits sorted in ascending order' + 'n with digits sorted in descending order'.

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 66, 77, 88, 99, 110, 121

Offset: 0

Patrick De Geest, Nov 15 1999

a(n) = A004185(n) + A004186(n). - Reinhard Zumkeller, Jun 07 2015

			E.g., n = 19 -> 19 + 91 = 110.

Zak Seidov and Michael De Vlieger, Table of n, a(n) for n = 0..9999 (First 1000 terms from Zak Seidov)
Nick Hobson, Python program for this sequence

Cf. A052009; different from A056964.

Cf. A004185, A004186, A271497.

a052008 n = a004185 n + a004186 n  -- Reinhard Zumkeller, Jun 07 2015

f[n_]:=Module[{sidn=Sort[IntegerDigits[n]]},FromDigits[sidn]+ FromDigits[ Reverse[sidn]]]; Array[f,70,0] (* Harvey P. Dale, Nov 13 2011 *)

for(n=0,100,D=digits(n);R=Vecrev(D);print1(sum(i=1,#D,10^(i-1)*(D[i]+R[i])),", ")) \\ Derek Orr, Feb 26 2017

A038574 Write n in ternary, sort digits into increasing order.

Original entry on oeis.org

0, 1, 2, 1, 4, 5, 2, 5, 8, 1, 4, 5, 4, 13, 14, 5, 14, 17, 2, 5, 8, 5, 14, 17, 8, 17, 26, 1, 4, 5, 4, 13, 14, 5, 14, 17, 4, 13, 14, 13, 40, 41, 14, 41, 44, 5, 14, 17, 14, 41, 44, 17, 44, 53, 2, 5, 8, 5, 14, 17, 8, 17, 26, 5, 14, 17, 14, 41, 44, 17, 44, 53, 8, 17, 26, 17, 44, 53, 26, 53, 80

Offset: 0

N. J. A. Sloane

			15 = 120 -> 012 = 5, so a(15)=5.

Seiichi Manyama, Table of n, a(n) for n = 0..10000
Michael Gilleland, Some Self-Similar Integer Sequences
Robert Walker, Self Similar Sloth Canon Number Sequences

Cf. A038573, A004185.

Table[FromDigits[Sort[IntegerDigits[n,3]],3],{n,0,90}] (* Harvey P. Dale, Dec 08 2015 *)

More terms from Erich Friedman.

A319652 Write n in 4-ary, sort digits into increasing order.

Original entry on oeis.org

0, 1, 2, 3, 1, 5, 6, 7, 2, 6, 10, 11, 3, 7, 11, 15, 1, 5, 6, 7, 5, 21, 22, 23, 6, 22, 26, 27, 7, 23, 27, 31, 2, 6, 10, 11, 6, 22, 26, 27, 10, 26, 42, 43, 11, 27, 43, 47, 3, 7, 11, 15, 7, 23, 27, 31, 11, 27, 43, 47, 15, 31, 47, 63, 1, 5, 6, 7, 5, 21, 22, 23, 6, 22, 26, 27

Offset: 0

Seiichi Manyama, Sep 25 2018

Seiichi Manyama, Table of n, a(n) for n = 0..4095

b-ary: A038573 (b=2), A038574 (b=3), this sequence (b=4), A319653 (b=5), A319654 (b=6), A319655 (b=7), A319656 (b=8), A319657 (b=9), A004185 (b=10).

Cf. A165012.

a:= n-> (l-> add(l[-i]*4^(i-1), i=1..nops(l)))(sort(convert(n, base, 4))):
seq(a(n), n=0..75);  # Alois P. Heinz, Aug 07 2024

Table[FromDigits[Sort[IntegerDigits[n, 4]], 4], {n, 0, 100}] (* Paolo Xausa, Aug 07 2024 *)

a(n) = fromdigits(vecsort(digits(n, 4)), 4); \\ Michel Marcus, Sep 25 2018

def A(k, n)
  (0..n).map{|i| i.to_s(k).split('').sort.join.to_i(k)}
end
p A(4, 100)

A319653 Write n in 5-ary, sort digits into increasing order.

Original entry on oeis.org

0, 1, 2, 3, 4, 1, 6, 7, 8, 9, 2, 7, 12, 13, 14, 3, 8, 13, 18, 19, 4, 9, 14, 19, 24, 1, 6, 7, 8, 9, 6, 31, 32, 33, 34, 7, 32, 37, 38, 39, 8, 33, 38, 43, 44, 9, 34, 39, 44, 49, 2, 7, 12, 13, 14, 7, 32, 37, 38, 39, 12, 37, 62, 63, 64, 13, 38, 63, 68, 69, 14, 39, 64, 69, 74, 3

Offset: 0

Seiichi Manyama, Sep 25 2018

Seiichi Manyama, Table of n, a(n) for n = 0..3124

b-ary: A038573 (b=2), A038574 (b=3), A319652 (b=4), this sequence (b=5), A319654 (b=6), A319655 (b=7), A319656 (b=8), A319657 (b=9), A004185 (b=10).

Cf. A165032, A319722.

Table[FromDigits[Sort[IntegerDigits[n,5]],5],{n,0,100}] (* Harvey P. Dale, Feb 29 2024 *)

a(n) = fromdigits(vecsort(digits(n, 5)), 5); \\ Michel Marcus, Sep 25 2018

def A(k, n)
  (0..n).map{|i| i.to_s(k).split('').sort.join.to_i(k)}
end
p A(5, 100)

A319654 Write n in 6-ary, sort digits into increasing order.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 1, 7, 8, 9, 10, 11, 2, 8, 14, 15, 16, 17, 3, 9, 15, 21, 22, 23, 4, 10, 16, 22, 28, 29, 5, 11, 17, 23, 29, 35, 1, 7, 8, 9, 10, 11, 7, 43, 44, 45, 46, 47, 8, 44, 50, 51, 52, 53, 9, 45, 51, 57, 58, 59, 10, 46, 52, 58, 64, 65, 11, 47, 53, 59, 65, 71, 2, 8

Offset: 0

Seiichi Manyama, Sep 25 2018

Seiichi Manyama, Table of n, a(n) for n = 0..7775

b-ary: A038573 (b=2), A038574 (b=3), A319652 (b=4), A319653 (b=5), this sequence (b=6), A319655 (b=7), A319656 (b=8), A319657 (b=9), A004185 (b=10).

Cf. A165051, A319723.

Table[FromDigits[Sort[IntegerDigits[n,6]],6],{n,0,80}] (* Harvey P. Dale, Sep 20 2020 *)

a(n) = fromdigits(vecsort(digits(n, 6)), 6); \\ Michel Marcus, Sep 25 2018

def A(k, n)
  (0..n).map{|i| i.to_s(k).split('').sort.join.to_i(k)}
end
p A(6, 100)

cp's OEIS Frontend

A036839 RATS(n): Reverse Add Then Sort the digits.

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A033860 Sort-then-add sequence: a(n+1) = a(n) + sort(a(n)).

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A070196 a(n) = n plus the sorted version of the base-10 digits of n.

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A069638 "Sorted" sum of two previous terms, beginning with 0,1. "Sorted" means to sort the digits of the sum in ascending order.

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A321540 3^n with digits rearranged into nondecreasing order.

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A052008 a(n) = 'n with digits sorted in ascending order' + 'n with digits sorted in descending order'.

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A038574 Write n in ternary, sort digits into increasing order.

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