A009996 -id:A009996 - cp's OEIS frontend

A004086 Read n backwards (referred to as R(n) in many sequences).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 21, 31, 41, 51, 61, 71, 81, 91, 2, 12, 22, 32, 42, 52, 62, 72, 82, 92, 3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 4, 14, 24, 34, 44, 54, 64, 74, 84, 94, 5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 6, 16, 26, 36, 46, 56, 66, 76, 86, 96, 7, 17, 27, 37, 47

Offset: 0

N. J. A. Sloane

Also called digit reversal of n.

Leading zeros (after the reversal has taken place) are omitted. - N. J. A. Sloane, Jan 23 2017

Indranil Ghosh, Table of n, a(n) for n = 0..50000 (first 1001 terms from Franklin T. Adams-Watters)
Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi, and Ruimin Zhang, Finding structure in sequences of real numbers via graph theory: a problem list, arXiv:2012.04625 [math.CO], Dec 08 2020.
Michael Penn, A digit moving number puzzle., YouTube video, 2022.

Cf. A004185, A004186, A009996, A073138, A188649, A221714.

Cf. A030101, A030102, A030103, A030104, A030105, A030107, A030108.

a004086 = read . reverse . show  -- Reinhard Zumkeller, Apr 11 2011

|.&.": i.@- 1e5 NB. Stephen Makdisi, May 14 2018

read transforms; A004086 := digrev; #cf "Transforms" link at bottom of page
A004086:=proc(n) local s,t; if n<10 then n else s:=irem(n,10,'t'); while t>9 do s:=s*10+irem(t,10,'t') od: s*10+t fi end; # M. F. Hasler, Jan 29 2012

Table[FromDigits[Reverse[IntegerDigits[n]]], {n, 0, 75}]
IntegerReverse[Range[0,80]](* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 13 2018 *)

dig(n) = {local(m=n,r=[]); while(m>0,r=concat(m%10,r);m=floor(m/10));r}
A004086(n) = {local(b,m,r);r=0;b=1;m=dig(n);for(i=1,matsize(m)[2],r=r+b*m[i];b=b*10);r} \\ Michael B. Porter, Oct 16 2009

A004086(n)=fromdigits(Vecrev(digits(n))) \\ M. F. Hasler, Nov 11 2010, updated May 11 2015, Sep 13 2019

def A004086(n):
    return int(str(n)[::-1]) # Chai Wah Wu, Aug 30 2014

For n > 0, a(a(n)) = n iff n mod 10 != 0. - Reinhard Zumkeller, Mar 10 2002
a(n) = d(n,0) with d(n,r) = r if n=0, otherwise d(floor(n/10), r*10+(n mod 10)). - Reinhard Zumkeller, Mar 04 2010
a(10*n+x) = x*10^m + a(n) if 10^(m-1) <= n < 10^m and 0 <= x <= 9. - Robert Israel, Jun 11 2015

Extended by Ray Chandler, Dec 30 2004

A010785 Repdigit numbers, or numbers whose digits are all equal.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999, 111111, 222222, 333333, 444444, 555555, 666666

Offset: 0

N. J. A. Sloane

Complement of A139819. - David Wasserman, May 21 2008
Subsequence of A134336 and of A178403. - Reinhard Zumkeller, May 27 2010
Subsequence of A193460. - Reinhard Zumkeller, Jul 26 2011
Intersection of A009994 and A009996. - David F. Marrs, Sep 29 2018
Beiler (1964) called these numbers "monodigit numbers". The term "repdigit numbers" was used by Trigg (1974). - Amiram Eldar, Jan 21 2022

Albert H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, p. 83.

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Eric F. Bravo, Carlos A. Gómez and Florian Luca, Product of Consecutive Tribonacci Numbers With Only One Distinct Digit, J. Int. Seq., Vol. 22 (2019), Article 19.6.3.
Eric Fernando Bravo, On concatenations of Padovan and Perrin numbers, Math. Commun. (2023) Vol 28, 105-119.
Mahadi Ddamulira, Repdigits as sums of three balancing numbers, Mathematica Slovaca, (2019), hal-02405969.
Mahadi Ddamulira, Padovan numbers that are concatenations of two distinct repdigits, arXiv:2003.10705 [math.NT], 2020.
Mahadi Ddamulira, Tribonacci numbers that are concatenations of two repdigits, hal-02547159, Mathematics [math] / Number Theory [math.NT], 2020.
Mahadi Ddamulira, Padovan numbers that are concatenations of two distinct repdigits, Mathematica Slovaca, Vol. 71, No. 2 (2021), pp. 275-284.
Bart Goddard and Jeremy Rouse, Sum of two repdigits a square, arXiv:1607.06681 [math.NT], 2016. Mentions this sequence.
Bir Kafle, Florian Luca and Alain Togbé, Triangular Repblocks, Fibonacci Quart., Vol. 56, No. 4 (2018), pp. 325-328.
Bir Kafle, Florian Luca and Alain Togbé, Pentagonal and heptagonal repdigits, Annales Mathematicae et Informaticae, Vol. 52 (2020), pp. 137-145.
Benedict Vasco Normenyo, Bir Kafle, and Alain Togbé, Repdigits as Sums of Two Fibonacci Numbers and Two Lucas Numbers, Integers, Vol. 19 (2019), Article A55.
Salah Eddine Rihane and Alain Togbé, Repdigits as products of consecutive Padovan or Perrin numbers, Arab. J. Math., Vol. 10 (2021), pp. 469-480.
Charles W. Trigg, Infinite sequences of palindromic triangular numbers, The Fibonacci Quarterly, Vol. 12, No. 2 (1974), pp. 209-212.
Eric Weisstein's World of Mathematics, Repdigit.
Wikipedia, Repdigit.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,0,-10).

Cf. A000005, A009994, A009996, A010879, A037904, A047842, A059995, A065444, A134336, A139819, A151949, A178401, A178403, A180410, A193459, A193460, A202022, A227362, A244112.

a010785 n = a010785_list !! n
a010785_list = 0 : r [1..9] where
   r (x:xs) = x : r (xs ++ [10*x + x `mod` 10])
-- Reinhard Zumkeller, Jul 26 2011

[(n-9*Floor((n-1)/9))*(10^Floor((n+8)/9)-1)/9: n in [0..50]]; // Vincenzo Librandi, Nov 10 2014

A010785 := proc(n)
    (n-9*floor(((n-1)/9)))*((10^(floor(((n+8)/9)))-1)/9) ;
end proc:
seq(A010785(n), n = 0 .. 100); # Robert Israel, Nov 09 2014

fQ[n_]:=Module[{id=IntegerDigits[n]}, Length[Union[id]]==1]; Select[Range[0,10000], fQ] (* Vladimir Joseph Stephan Orlovsky, Dec 29 2010 *)
Union[FromDigits/@Flatten[Table[PadRight[{},i,n],{n,0,9},{i,6}],1]] (* or *) LinearRecurrence[{0,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,0,-10}, {0,1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88},40] (* Harvey P. Dale, Dec 28 2011 *)
Union@ Flatten@ Table[k (10^n - 1)/9, {k, 0, 9}, {n, 6}] (* Robert G. Wilson v, Oct 09 2014 *)
Table[(n - 9 Floor[(n-1)/9]) (10^Floor[(n+8)/9] - 1)/9, {n, 0, 50}] (* José de Jesús Camacho Medina, Nov 06 2014 *)

a(n)=10^((n+8)\9)\9*((n-1)%9+1) \\ Charles R Greathouse IV, Jun 15 2011

nxt(n,t=n%10)=if(t<9,n*(t+1),n*10+9)\t \\ Yields the term a(k+1) following a given term a(k)=n. M. F. Hasler, Jun 24 2016

is(n)={1==#Set(digits(n))}
inv(n) = 9*#Str(n) + n%10 - 9 \\ David A. Corneth, Jun 24 2016

def a(n): return 0 if n == 0 else int(str((n-1)%9+1)*((n-1)//9+1))
print([a(n) for n in range(55)]) # Michael S. Branicky, Dec 29 2021

print([0]+[int(d*r) for r in range(1, 7) for d in "123456789"]) # Michael S. Branicky, Dec 29 2021

# without string operations
def a(n): return 0 if n == 0 else (10**((n-1)//9+1)-1)//9*((n-1)%9+1)
print([a(n) for n in range(55)]) # Michael S. Branicky, Nov 03 2023

A037904(a(n)) = 0. - Reinhard Zumkeller, Dec 14 2007
A178401(a(n)) > 0. - Reinhard Zumkeller, May 27 2010
From Reinhard Zumkeller, Jul 26 2011: (Start)
For n > 0: A193459(a(n)) = A000005(a(n)).
for n > 10: a(n) mod 10 = floor(a(n)/10) mod 10.
A010879(n) = A010879(A059995(n)). (End)
A202022(a(n)) = 1. - Reinhard Zumkeller, Dec 09 2011
a(0)=0, a(1)=1, a(2)=2, a(3)=3, a(4)=4, a(5)=5, a(6)=6, a(7)=7, a(8)=8, a(9)=9, a(10)=11, a(11)=22, a(12)=33, a(13)=44, a(14)=55, a(15)=66, a(16)=77, a(17)=88, a(n) = 11*a(n-9) - 10*a(n-18). - Harvey P. Dale, Dec 28 2011
A151949(a(n)) = 0; A180410(a(n)) = A227362(a(n)). - Reinhard Zumkeller, Jul 09 2013
a(n) = (n - 9*floor((n-1)/9))*(10^floor((n+8)/9) - 1)/9. - José de Jesús Camacho Medina, Nov 06 2014
G.f.: x*(1+2*x+3*x^2+4*x^3+5*x^4+6*x^5+7*x^6+8*x^7+9*x^8)/((1-x^9)*(1-10*x^9)). - Robert Israel, Nov 09 2014
A047842(a(n)) = A244112(a(n)). - Reinhard Zumkeller, Nov 11 2014
Sum_{n>=1} 1/a(n) = (7129/2520) * A065444 = 3.11446261209177581335... - Amiram Eldar, Jan 21 2022

Name clarified by Jon E. Schoenfield, Nov 10 2023

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

Original entry on oeis.org

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

A004186 Arrange digits of n in decreasing order.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 31, 41, 51, 61, 71, 81, 91, 20, 21, 22, 32, 42, 52, 62, 72, 82, 92, 30, 31, 32, 33, 43, 53, 63, 73, 83, 93, 40, 41, 42, 43, 44, 54, 64, 74, 84, 94, 50, 51, 52, 53, 54, 55, 65, 75, 85, 95, 60, 61, 62, 63, 64, 65, 66, 76, 86, 96, 70, 71, 72

Offset: 0

N. J. A. Sloane

a(A009996(n)) = A009996(n). - Reinhard Zumkeller, Oct 31 2007

If we define "sortable primes" as prime numbers that remain prime when their digits are sorted in decreasing order, then all absolute primes (A003459) are sortable primes but not all sortable primes are absolute primes. For example, 113 is both sortable and absolute, and 313 is sortable but not absolute since its digits can be permuted to 133 = 7 * 19. - Alonso del Arte, Oct 05 2013

			a(19) = 91 because the digits of 19 being 1 and 9, arranged in decreasing order they are 9 and 1.
a(20) = 20 because the digits are already in decreasing order.

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

Cf. A004185, A004086, A009996, A064222, A194233, A032553, A032554, A028907, A028908.

import Data.List (sort)
a004186 = read . reverse . sort . show :: Integer -> Integer
-- Reinhard Zumkeller, Aug 19 2011

A004186 := proc(n)
    local dgs;
    convert(n,base,10) ;
    dgs := sort(%) ;
    add( op(i,dgs)*10^(i-1),i=1..nops(dgs)) ;
end proc:
seq(A004186(n),n=0..20) ; # R. J. Mathar, Jul 26 2015

sortDigitsDown[n_] := FromDigits@ Reverse@ Sort@ IntegerDigits@ n; Array[sortDigitsDown, 73, 0] (* Robert G. Wilson v, Aug 19 2011 *)

reconstruct(m) = {local(r); r=0; for(i=1,matsize(m)[2],r=r*10+m[i]); r}
A004186(n) = reconstruct(vecsort(digits(n),,4))
\\ Michael B. Porter, Nov 11 2009

a(n) = fromdigits(vecsort(digits(n), , 4)); \\ Joerg Arndt, Feb 24 2019

def a(n): return int("".join(sorted(str(n), reverse=True)))
print([a(n) for n in range(73)]) # Michael S. Branicky, Feb 21 2021

n <= a(n) < 10n. - Charles R Greathouse IV, Aug 07 2024

More terms from Reinhard Zumkeller, Oct 31 2007

A372034 For a positive number k, let L(k) denote the list consisting of k followed by the prime factors of k, with repetition, in nondecreasing order; sequence gives composite k such that the digits of L(k) are in nonincreasing order.

Original entry on oeis.org

4, 8, 9, 22, 32, 33, 44, 55, 64, 77, 88, 93, 99, 422, 633, 775, 844, 933, 993, 4222, 4442, 6333, 6655, 6663, 7533, 7744, 7775, 8444, 8884, 9663, 9993, 44222, 66333, 88444, 99633, 99933, 99993, 933333, 966333, 996663, 999993, 4442222, 6663333, 7777775, 8884444, 9663333, 9666633, 9666663

Offset: 1

Scott R. Shannon, Apr 16 2024

Is it true that no terms end with 1? A separate search on those shows none with < 70 digits. Michael S. Branicky, Apr 23 2024

Testing all products of repunit primes (A004022, A004023), there are no terms ending in 1 less than 10^3000. - Michael S. Branicky, Apr 24 2024

			The initial terms and their factorizations are:
4 = [2, 2]
8 = [2, 2, 2]
9 = [3, 3]
22 = [2, 11]
32 = [2, 2, 2, 2, 2]
33 = [3, 11]
44 = [2, 2, 11]
55 = [5, 11]
64 = [2, 2, 2, 2, 2, 2]
77 = [7, 11]
88 = [2, 2, 2, 11]
93 = [3, 31]
99 = [3, 3, 11]
422 = [2, 211]
633 = [3, 211]
775 = [5, 5, 31]
844 = [2, 2, 211]
933 = [3, 311]
993 = [3, 331]
4222 = [2, 2111]
4442 = [2, 2221]
6333 = [3, 2111]
6655 = [5, 11, 11, 11]
6663 = [3, 2221]
7533 = [3, 3, 3, 3, 3, 31]
7744 = [2, 2, 2, 2, 2, 2, 11, 11]
...

Michael S. Branicky, Table of n, a(n) for n = 1..197 (all terms with <= 21 digits)

Cf. A004022, A004023, A009996, A028867, A372053, A372029, A027746, A372055.

from sympy import factorint, isprime
def ni(s): return sorted(s, reverse=True) == list(s)
def ok(n):
    if n < 4 or isprime(n): return False
    s, f = str(n), "".join(str(p)*e for p, e in factorint(n).items())
    return ni(s+f)
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Apr 23 2024

# faster for initial segment of sequence
from sympy import factorint, isprime
from itertools import islice, combinations_with_replacement as mc
def ni(s): return s == "".join(sorted(s, reverse=True))
def bgen(d):
    yield from ("".join(m) for m in mc("987654321", d))
def agen(): # generator of terms
    for d in range(1, 70):
        out = set()
        for s in bgen(d):
            t = int(s)
            if t < 4 or isprime(t): continue
            if ni(s+"".join(str(p)*e for p, e in factorint(t).items())):
                out.add(t)
        yield from sorted(out)
print(list(islice(agen(), 50))) # Michael S. Branicky, Apr 23 2024

A152054 Bouncy numbers (numbers whose digits are in neither increasing nor decreasing order).

Original entry on oeis.org

101, 102, 103, 104, 105, 106, 107, 108, 109, 120, 121, 130, 131, 132, 140, 141, 142, 143, 150, 151, 152, 153, 154, 160, 161, 162, 163, 164, 165, 170, 171, 172, 173, 174, 175, 176, 180, 181, 182, 183, 184, 185, 186, 187, 190, 191, 192, 193, 194, 195, 196

Offset: 1

Jerome Abela (Jerome.Abela(AT)gmail.com), Nov 22 2008

Complement of union of A009994 and A009996. - Ray Chandler, Oct 25 2011

Number of n-digit bouncy numbers is 9*10^(n-1) - (n+18)*binomial(n+8, 8)/9 + 10. - Altug Alkan, Oct 02 2018

David F. Marrs, Table of n, a(n) for n = 1..10000
Project Euler, Non-bouncy numbers Problem 113

Cf. A152464. - Jon E. Schoenfield, Dec 06 2008

Cf. A009994, A009996, A204692.

Select[Range[0,200], !LessEqual@@IntegerDigits[#] && !GreaterEqual@@IntegerDigits[#]&] (* Ray Chandler, Oct 25 2011 *)
bnQ[n_]:=Module[{didn=Differences[IntegerDigits[n]]},Count[didn,?(#>0&)]>0 && Count[didn,?(#<0&)]>0]; Select[Range[100,200],bnQ] (* Harvey P. Dale, Jun 13 2020 *)

a = 1
b = 100
while a != 51:
    if str(b) != ''.join(sorted(str(b))) and str(b) != ''.join(sorted(str(b)))[::-1]:
        print(b)
        a += 1
    b += 1
# David F. Marrs, Sep 25 2018

from itertools import count, islice
def A152054_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        l = len(s:=tuple(int(d) for d in str(n)))
        for i in range(1,l-1):
            if (s[i-1]-s[i])*(s[i]-s[i+1]) < 0:
                yield n
                break
A152054_list = list(islice(A152054_gen(),30)) # Chai Wah Wu, Jul 28 2023

More terms from Jon E. Schoenfield, Dec 06 2008

A028822 Squares with digits in nonincreasing order.

Original entry on oeis.org

0, 1, 4, 9, 64, 81, 100, 400, 441, 841, 900, 961, 6400, 7744, 8100, 10000, 40000, 44100, 84100, 90000, 96100, 640000, 774400, 810000, 1000000, 4000000, 4410000, 8410000, 8874441, 9000000, 9610000, 9853321, 64000000, 77440000

Offset: 1

Patrick De Geest

From Robert G. Wilson v, Jan 02 2014: (Start)
If x is present so is 100x. The primitives are 0, 1, 4, 9, 64, 81, 441, 841, 961, 7744, 8874441, 9853321, 999887641, …, . = A062826. Their square roots are: 0, 1, 2, 3, 8, 9, 21, 29, 31, 88, 2979, 3139, 31621, …, . Are there no more primitives?
Number of terms less than 10^k, beginning with k=0: 1, 4, 6, 12, 15, 21, 24, 32, 35, 44, 47, 56, 59, 68, 71, 80, 83, 92, 95, …, .
Like all squares the ending digits can be 0, 1, 4, 5, 6 or 9. Here is the tally of the list of terms < 10^18: {0, 84}, {1, 8}, {4, 3}, {5, 0}, {6, 0}, {9, 1}. (End)

Robert G. Wilson v, Table of n, a(n) for n = 1..96
Patrick De Geest, Palindromic Squares in bases 2 to 17

Cf. A062826, A028820, A028821, A009996.

fQ[n_] := Max[ Differences[ IntegerDigits[ n]]] < 1; Select[ Range[0, 9000]^2, fQ] (* Robert G. Wilson v, Jan 02 2014 *)
Select[Range[0,10^4]^2,GreaterEqual@@IntegerDigits[#]&] (* Ray Chandler, Jan 05 2014 *)

isA009996(n)=n=digits(n); for(i=2,#n,if(n[i]>n[i-1],return(0))); 1
is(n)=issquare(n) && isA009996(n) \\ Charles R Greathouse IV, Jan 02 2014

For n > 1, a(n) = A062826(i) * 10^j for some i and j. - Charles R Greathouse IV, Jan 02 2014

a(n) = A028821(n)^2. - Ray Chandler, Jan 05 2014

Better name from Robert G. Wilson v, Jan 02 2014

A032907 Numbers whose base-10 representation Sum_{i=0..m} d(i)*10^i has d(0) <= d(1) >= d(2) <= ...

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21, 22, 30, 31, 32, 33, 40, 41, 42, 43, 44, 50, 51, 52, 53, 54, 55, 60, 61, 62, 63, 64, 65, 66, 70, 71, 72, 73, 74, 75, 76, 77, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 110, 111, 120

Offset: 1

Clark Kimberling

David A. Corneth, Table of n, a(n) for n = 1..5343 (all terms < 20000)

Differs from A032873 and A009996.

is(n)=my(d=digits(n));r=1;forstep(i=#d,2,-1,if((-1)^(#d-i)*d[i]>(-1)^(#d-i)*d[i-1],r=0;break));r \\ David A. Corneth, Feb 01 2015

A032873 Numbers whose base-10 representation Sum_{i=0..m} d(i)*10^i has d(m) >= d(m-1) <= d(m-2) >= ...

Original entry on oeis.org

Offset: 1

Clark Kimberling

Contains 100 so differs from A032907, contains 101 so differs from A009996.

A072543 Numbers whose largest decimal digit is also the initial digit.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21, 22, 30, 31, 32, 33, 40, 41, 42, 43, 44, 50, 51, 52, 53, 54, 55, 60, 61, 62, 63, 64, 65, 66, 70, 71, 72, 73, 74, 75, 76, 77, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 110, 111, 200, 201

Offset: 1

Reinhard Zumkeller, Aug 04 2002

A054055(a(n)) = A000030(a(n));

the sequence differs from A009996, A032873 and A032907: a(66)=101 is not in A009996, a(67)=110 is not in A032873 and a(65)=100 is not in A032907.

			a(10^ 1) = 9
a(10^ 2) = 411
a(10^ 3) = 6216
a(10^ 4) = 73474
a(10^ 5) = 813826
a(10^ 6) = 8512170
a(10^ 7) = 88368780
a(10^ 8) = 911960211
a(10^ 9) = 9237655227
a(10^10) = 93323313303

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

Cf. A072544.

a072543 n = a072543_list !! (n-1)
a072543_list = [x | x <- [0..], a054055 x == a000030 x]
-- Reinhard Zumkeller, Apr 25 2012

for i from 1 to 10 do A[i]:= i-1 od:
count:= 10:
for i from 1 to 9 do P[i]:= [seq([j],j=0..i)]; od:
for d from 2 to 4 do
  for x from 1 to 9 do
    for p in P[x] do
      count:= count+1;
      A[count]:= add(p[k]*10^(k-1),k=1..d-1) + x*10^(d-1);
    od:
    P[x]:= [seq(seq([op(v),t], v=P[x]),t=0..x)];
  od
od:
seq(A[i],i=1..count); # Robert Israel, Feb 01 2015

Select[Range[0,250],Max[IntegerDigits[#]]==First[IntegerDigits[#]]&] (* Harvey P. Dale, Apr 28 2016 *)

is(n)=n=digits(n); !#n || n[1]==vecmax(n) \\ Charles R Greathouse IV, Jan 02 2014

a(n)={d = 0; r = 1; s = 0; i = 0; if(n == 1, 0, n-=2; while(n > sum(i=0, 9,(i+1)^d), n-=sum(i=0, 9, (i+1)^d); n++; d++); while(n >= (r+1)^d, n -= (r+1)^d; r++);s = r * 10^d; while(n, s += 10^i*(n%(r+1)); n \= (r+1); i++));s } \\ David A. Corneth, Jan 31 2015

Offset corrected by Reinhard Zumkeller, Apr 25 2012

cp's OEIS Frontend

A004086 Read n backwards (referred to as R(n) in many sequences).

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A010785 Repdigit numbers, or numbers whose digits are all equal.

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

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A004186 Arrange digits of n in decreasing order.

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A372034 For a positive number k, let L(k) denote the list consisting of k followed by the prime factors of k, with repetition, in nondecreasing order; sequence gives composite k such that the digits of L(k) are in nonincreasing order.

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