A004186 -id:A004186 - cp's OEIS frontend

A032553 Arrange digits of cubes in ascending order.

0, 1, 8, 27, 46, 125, 126, 334, 125, 279, 1, 1133, 1278, 1279, 2447, 3357, 469, 1349, 2358, 5689, 8, 1269, 1468, 11267, 12348, 12556, 15677, 13689, 12259, 23489, 27, 12799, 23678, 33579, 3349, 24578, 45666, 3556, 24578, 13599, 46

Offset: 0

Patrick De Geest, Apr 15 1998

			Leading zeros discarded (e.g., 40^3 = 64000 = 00046 becomes 46).

Enrique Pérez Herrero, Table of n, a(n) for n = 0..1000

Cf. A032554.
Cf. A028907, A028908.
Cf. A004186, A004185.

Table[FromDigits[Sort[IntegerDigits[n^3]]],{n,0,40}] (* Enrique Pérez Herrero, Sep 29 2013 *)

A032554 Arrange digits of cubes in descending order.

Original entry on oeis.org

0, 1, 8, 72, 64, 521, 621, 433, 521, 972, 1000, 3311, 8721, 9721, 7442, 7533, 9640, 9431, 8532, 9865, 8000, 9621, 86410, 76211, 84321, 65521, 77651, 98631, 95221, 98432, 72000, 99721, 87632, 97533, 94330, 87542, 66654, 65530, 87542, 99531

Offset: 0

Patrick De Geest, Apr 15 1998

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A000578, A004186, A032553.

f:= proc(n) local L,i;
  L:= sort(convert(n^3,base,10));
  add(L[i]*10^(i-1),i=1..nops(L))
end proc:
map(f, [$0..100]); # Robert Israel, Mar 12 2020

Table[FromDigits[Sort[IntegerDigits[n^3],Greater]],{n,0,40}] (* Harvey P. Dale, Nov 14 2021 *)

a(n) = A004186(A000578(n)). - Michel Marcus, Mar 12 2020

A096089 Let f(n) = largest number formed using digits of n, g(n) = smallest number formed using digits of n; then a(n) = floor(f(n)/g(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 2, 2, 3, 3, 4, 4, 4, 10, 1, 1, 1, 1, 2, 2, 2, 2, 3, 10, 2, 1, 1, 1, 1, 1, 1, 2, 2, 10, 2, 1, 1, 1, 1, 1, 1, 1, 1, 10, 3, 2, 1, 1, 1, 1, 1, 1, 1, 10, 3, 2, 1, 1, 1, 1, 1, 1, 1, 10, 4, 2, 1, 1, 1, 1, 1, 1, 1, 10, 4, 2, 2, 1, 1, 1, 1, 1, 1, 10, 4, 3, 2, 1, 1, 1, 1, 1, 1, 100, 10, 17, 23, 29, 34

Offset: 1

Amarnath Murthy, Jun 22 2004

			a(12324) = floor(43221/12234) = 3.
a(1098) = floor(9810/0189) = 51.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A004186, A004185, A096090, A096091.

A096089 := proc(n)
    floor( A004186(n)/A004185(n)) ;
end proc: # R. J. Mathar, Jul 26 2015

a(n) = d = digits(n); fromdigits(vecsort(d, , 4)) \ fromdigits(vecsort(d))

More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Jul 19 2004

a(1)..a(9) prepended by David A. Corneth, Jan 21 2019

A108782 Difference between n and the largest number with the same digit set as n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 18, 27, 36, 45, 54, 63, 72, 0, 0, 0, 9, 18, 27, 36, 45, 54, 63, 0, 0, 0, 0, 9, 18, 27, 36, 45, 54, 0, 0, 0, 0, 0, 9, 18, 27, 36, 45, 0, 0, 0, 0, 0, 0, 9, 18, 27, 36, 0, 0, 0, 0, 0, 0, 0, 9, 18, 27, 0, 0, 0, 0, 0, 0, 0, 0, 9, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0

Offset: 0

Zak Seidov, Jun 29 2005

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A004186, A151949, A193581.

FromDigits[Sort[IntegerDigits[n], Greater]] - n (Rob Pratt)
Table[Max[FromDigits/@ Permutations[IntegerDigits[n]]]-n, {n, 150}]

a(n) = A004186(n) - n. - Seiichi Manyama, Sep 25 2018

a(0)=0 prepended by Seiichi Manyama, Sep 25 2018

A194233 Smallest number greater than n with exactly the same digits as n in decimal representation, a(n)=10*n if no such number exists.

Original entry on oeis.org

10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 21, 31, 41, 51, 61, 71, 81, 91, 200, 210, 220, 32, 42, 52, 62, 72, 82, 92, 300, 310, 320, 330, 43, 53, 63, 73, 83, 93, 400, 410, 420, 430, 440, 54, 64, 74, 84, 94, 500, 510, 520, 530, 540, 550, 65, 75, 85, 95

Offset: 1

Reinhard Zumkeller, Aug 19 2011

A004186(a(n)) = A004186(n) or A004186(a(n)) = 10*A004186(n).

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

import Data.List (find); import Data.Maybe (fromMaybe)
a194233 n =
   fromMaybe (10*n) $ find (== a004186 n) $ map a004186 [n+1..10*n]

A211655 Down-sortable primes: Primes that are also primes after digits are sorted into decreasing order.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 31, 37, 41, 43, 53, 61, 71, 73, 79, 83, 97, 113, 131, 149, 157, 163, 167, 179, 181, 191, 197, 199, 211, 241, 251, 281, 311, 313, 331, 337, 347, 359, 373, 389, 419, 421, 431, 433, 443, 461, 463, 491, 521, 541, 563, 571, 593, 613, 617, 631, 641, 643, 653

Offset: 1

Francis J. McDonnell, Apr 17 2012

All 1- and 2-digit reversible primes (A007500) are trivially in this sequence. No primes from A056709 are in this sequence. Clearly all absolute primes (A003459) are sortable primes but not all sortable primes are absolute primes. - Alonso del Arte, Oct 08 2013

			131 is prime and after sorting its digits into nonincreasing order we obtain 311, which is prime.
163 is in the sequence because its digits sorted in decreasing order give 631, which is prime. (Note that this is not a reversible prime, since 361 = 19^2.)

Francis J. McDonnell, Table of n, a(n) for n = 1..10000
Francis J. McDonnell, Java Program

Cf. A004186, A211654, A028864, A028867.

Select[Prime[Range[200]], PrimeQ[FromDigits[-Sort[-IntegerDigits[#]]]] &] (* T. D. Noe, Apr 17 2012 *)

A351988 In the factorial base expansion of n, arrange digits in decreasing order.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 8, 9, 14, 15, 12, 14, 14, 15, 16, 17, 18, 20, 20, 21, 22, 23, 24, 30, 30, 32, 54, 56, 30, 32, 32, 33, 56, 57, 54, 56, 56, 57, 62, 63, 78, 80, 80, 81, 86, 87, 48, 54, 54, 56, 60, 62, 54, 56, 56, 57, 62, 63, 60, 62, 62, 63, 64, 65, 84, 86

Offset: 0

Rémy Sigrist, Feb 27 2022

This sequence is to factorial base what A004186 is to decimal base.

			For n = 1664:
- the factorial base expansion of 1664 is "214110",
- arranging these digits in decreasing order gives "421110",
- so a(1664) = 4*6! + 2*5! + 1*4! + 1*3! + 1*2! + 0*1! = 3152.

Cf. A004186 (decimal analog), A073138 (binary analog), A108731, A319651 (ternary analog), A351987.

max = 5; b = MixedRadix[Range[max, 2, -1]]; a[n_] := FromDigits[Sort[IntegerDigits[n, b], Greater], b]; Array[a, max!, 0] (* Amiram Eldar, Feb 28 2022 *)

a(n) = { my (dd=[]); for (r=2, oo, if (n==0, dd = vecsort(dd); return (sum(k=1, #dd, dd[k]*k!)), dd = concat(dd, n%r); n\=r)) }

a(a(n)) = a(n).

a(n) >= n with equality iff n belongs to A351987.

A371653 Numbers k such that the number formed by putting the digits of k in descending order is prime.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 14, 16, 17, 31, 34, 35, 37, 38, 41, 43, 53, 61, 71, 73, 79, 83, 97, 112, 113, 118, 119, 121, 124, 125, 128, 131, 133, 134, 136, 142, 143, 145, 146, 149, 152, 154, 157, 163, 164, 166, 167, 175, 176, 179, 181, 182, 188, 191, 194, 197, 199

Offset: 1

César Eliud Lozada, Apr 01 2024

Numbers k such that A004186(k) is prime. - Robert Israel, Apr 01 2024

If N is a term then all numbers with the same digits as N are terms too.

			142 is a term because its digits in decreasing order form 421 and this is prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A004186, A007500, A095179, A371654.

dd:= proc(n) local L,i;
   L:= sort(convert(n,base,10));
   add(L[i]*10^(i-1),i=1..nops(L))
end proc:
select(isprime @ dd, [$1..1000]); # Robert Israel, Apr 01 2024

Select[Range[500], PrimeQ[FromDigits[ReverseSort[IntegerDigits[#]]]] &]

from sympy import isprime
def ok(n): return isprime(int("".join(sorted(str(n), reverse=True))))
print([k for k in range(200) if ok(k)]) # Michael S. Branicky, Apr 01 2024

from itertools import count, islice, combinations_with_replacement
from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def A371653_gen(): # generator of terms
    for l in count(1):
        xlist = []
        for p in combinations_with_replacement('987654321',l):
            if isprime(int(''.join(p))):
                xlist.extend(int(''.join(d)) for d in multiset_permutations(p))
        yield from sorted(xlist)
A371653_list = list(islice(A371653_gen(),30)) # Chai Wah Wu, Apr 10 2024

A337925 Digits of n rearranged to be the smallest number with the fewest possible prime factors, counted with multiplicity. Terms retain the same number of digits as n, i.e. leading digits may not be zero.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 13, 41, 15, 61, 17, 18, 19, 20, 21, 22, 23, 42, 25, 26, 27, 82, 29, 30, 13, 23, 33, 43, 53, 63, 37, 83, 39, 40, 41, 42, 43, 44, 45, 46, 47, 84, 49, 50, 15, 25, 53, 45, 55, 65, 57, 58, 59, 60, 61, 26, 63, 46, 65, 66, 67, 86, 69, 70, 17, 27, 37, 47, 57, 67, 77

Offset: 1

Roderick Kimball, Sep 30 2020

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Cf. A001222, A004186, A328447.

a[n_] := Module[{p = FromDigits /@ Select[Permutations @ IntegerDigits[n], First[#] > 0 &]}, o = PrimeOmega[p]; Min[p[[Position[o, Min[o]] // Flatten]]]]; Array[a, 100] (* Amiram Eldar, Oct 19 2020 *)

a(n) = {my(d = digits(n), v = select(x->#(digits(x))==#d, vector((#d)!, i, fromdigits(vector(#d, k, d[numtoperm(#d, i-1)[k]])))), b = vecmin(vector(#v, k, bigomega(v[k])))); vecmin(select(x->(bigomega(x)==b), v));} \\ Michel Marcus, Oct 19 2020

a(a(n)) = a(n). - Rémy Sigrist, Oct 22 2020

A273003 Arrange the base 10 digits of the n-th Fibonacci number in descending order.

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 31, 21, 43, 55, 98, 441, 332, 773, 610, 987, 9751, 8542, 8411, 7665, 96410, 77111, 87652, 86643, 75520, 933211, 986411, 873111, 954221, 843200, 9664321, 9873210, 8755432, 8877520, 9765422, 95433210, 87754211, 99886310, 98665432

Offset: 0

Alonso del Arte, May 12 2016

Conjecture: the largest Fibonacci number F(n) with its base 10 digits already sorted in descending order is F(16) = 987.

			a(7) = 31 because F(7) = 13, so the digits in descending order become 31.
a(8) = 21 = F(8), the digits are already in descending order.

Cf. A000045, A004186, A272918, A273046.

FromDigits[Reverse[Sort[IntegerDigits[#]]]]&/@Fibonacci[Range[0,50]] (* Harvey P. Dale, Sep 16 2016 *)

a(n)=fromdigits(vecsort(digits(fibonacci(n)),,4)) \\ Charles R Greathouse IV, May 15 2016

a(n) = A004186(A000045(n)). - Michel Marcus, May 15 2016

Corrected and extended by Harvey P. Dale, Sep 16 2016

cp's OEIS Frontend

A032553 Arrange digits of cubes in ascending order.

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Mathematica

A032554 Arrange digits of cubes in descending order.

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Maple

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A096089 Let f(n) = largest number formed using digits of n, g(n) = smallest number formed using digits of n; then a(n) = floor(f(n)/g(n)).

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A108782 Difference between n and the largest number with the same digit set as n.

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A194233 Smallest number greater than n with exactly the same digits as n in decimal representation, a(n)=10*n if no such number exists.

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Haskell

A211655 Down-sortable primes: Primes that are also primes after digits are sorted into decreasing order.

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Mathematica

A351988 In the factorial base expansion of n, arrange digits in decreasing order.

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Mathematica

PARI

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A371653 Numbers k such that the number formed by putting the digits of k in descending order is prime.

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