A071589 -id:A071589 - cp's OEIS frontend

A227362 Distinct digits of n arranged in decreasing order.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 21, 31, 41, 51, 61, 71, 81, 91, 20, 21, 2, 32, 42, 52, 62, 72, 82, 92, 30, 31, 32, 3, 43, 53, 63, 73, 83, 93, 40, 41, 42, 43, 4, 54, 64, 74, 84, 94, 50, 51, 52, 53, 54, 5, 65, 75, 85, 95, 60, 61, 62, 63, 64, 65, 6, 76, 86

Offset: 0

Reinhard Zumkeller, Jul 09 2013

a(n) <= 9876543210; a(a(n)) = a(n);
A055642(a(n)) <= 10;
A055642(a(n)) <= A055642(n), A055642(a(n)) = A055642(n) iff A178788(n) = 1;
a(A109303(n)) < A109303(n); a(A009995(n)) = A009995(n); a(A071589(n)) > A071589(n);
a(n) = A151949(n) + A180410(n).

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

Cf. A004186, A230959.

import Data.List (nub, sort)
a227362 = read . reverse . sort . nub . show :: Integer -> Integer

a:= n-> parse(cat(sort([{convert(n, base, 10)[]}[]], `>`)[])):
seq(a(n), n=0..68);  # Alois P. Heinz, Sep 21 2022

f[n_] := FromDigits[Reverse@ Union@ IntegerDigits@ n]; f /@ Range[0, 68] (* Michael De Vlieger, Apr 16 2015, corrected by Robert G. Wilson v *)

a(n) = {if (n == 0, d = [0], d = digits(n)); eval(subst(Pol(vecsort(d,,12)), x, 10));} \\ Michel Marcus, Apr 16 2015

a(n)=fromdigits(vecsort(digits(n),,12)) \\ Charles R Greathouse IV, Apr 16 2015

def A227362(n): return int(''.join(sorted(set(str(n)),reverse=True))) # Chai Wah Wu, Nov 23 2022

A071590 Numbers k such that reversal(k) < k.

Original entry on oeis.org

10, 20, 21, 30, 31, 32, 40, 41, 42, 43, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 201, 210, 211, 220, 221, 230, 231

Offset: 1

Benoit Cloitre, Jun 01 2002

David A. Corneth, Table of n, a(n) for n = 1..5400 (first 1000 terms from T. D. Noe)

Cf. A004086 (digit reversal), A071589 (reversal(k) > k), A002113 (reversal(k) = k).

Cf. A161602 (binary reversal(k) < k).

Select[Range[300], # > FromDigits[Reverse[IntegerDigits[#]]] &] (* T. D. Noe, Mar 14 2012 *)
Select[Range[300],IntegerReverse[#]<#&] (* Harvey P. Dale, Jan 16 2022 *)

for(i=2,300,n=(i); s=ceil(log(n)/log(10)); if((sum(i=0,s,10^(s-i-1)*(floor(n/10^i*1.)-10*floor(n/10^(i+1)*1.))))

is(n) = {fromdigits(Vecrev(digits(n)))David A. Corneth, Apr 07 2021

def ok(n): return int(str(n)[::-1]) < n
print([k for k in range(232) if ok(k)]) # Michael S. Branicky, Oct 20 2021

Definition corrected by Harvey P. Dale, Jan 16 2022

A297272 Numbers whose base-10 digits have greater up-variation than down-variation; see Comments.

Original entry on oeis.org

12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 34, 35, 36, 37, 38, 39, 45, 46, 47, 48, 49, 56, 57, 58, 59, 67, 68, 69, 78, 79, 89, 102, 103, 104, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 128

Offset: 1

Clark Kimberling, Jan 16 2018

Suppose that n has base-b digits b(m), b(m-1), ..., b(0). The base-b down-variation of n is the sum DV(n,b) of all d(i)-d(i-1) for which d(i) > d(i-1); the base-b up-variation of n is the sum UV(n,b) of all d(k-1)-d(k) for which d(k) < d(k-1). The total base-b variation of n is the sum TV(n,b) = DV(n,b) + UV(n,b). See the guide at A297330.

Differs from A071589 first at 1011 which is in A071589 but not in here because UV(1011) = DV(1011)=1. - R. J. Mathar, Jan 23 2018

			198765 in base-10:  1,9,8,7,6,5, having DV = 4, UV = 8, so that 198765 is in the sequence.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A297330, A297270, A297271.

g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
b = 10; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
Take[Flatten[Position[w, -1]], 120]   (* A297270 *)
Take[Flatten[Position[w, 0]], 120]    (* A297271 *)
Take[Flatten[Position[w, 1]], 120]    (* A297272 *)

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A227362 Distinct digits of n arranged in decreasing order.

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A071590 Numbers k such that reversal(k) < k.

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A297272 Numbers whose base-10 digits have greater up-variation than down-variation; see Comments.

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