A054055 -id:A054055 - cp's OEIS frontend

A068505 Decimal representation of n interpreted in base b+1, where b=A054055(n) is the largest digit in decimal representation of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 6, 7, 8, 11, 14, 17, 20, 23, 26, 29, 12, 13, 14, 15, 19, 23, 27, 31, 35, 39, 20, 21, 22, 23, 24, 29, 34, 39, 44, 49, 30, 31, 32, 33, 34, 35, 41, 47, 53, 59, 42, 43, 44, 45, 46, 47, 48, 55, 62, 69, 56, 57, 58, 59, 60, 61

Offset: 1

Reinhard Zumkeller, Mar 11 2002, Feb 23 2008

a(n) = n iff n < 10 OR n is a "9ish number": a(A011539(n)) = A011539(n). - Reinhard Zumkeller, Dec 29 2011

			a(20)=2*3^1+0*1=6, a(21)=2*3^1+1*1=7, a(22)=2*3^1+2*1=8,
a(23)=2*4^1+3*1=11, a(24)=2*5^1+4*1=14, a(25)=2*6^1+5*1=17,
a(26)=2*7^1+6*1=20, a(27)=2*8^1+7*1=23, a(28)=2*9^1+8*1=26,
a(29)=2*10^1+9*1=29, a(30)=3*4^1+0*1=12, a(31)=3*4^1+1*1=13.

R. Zumkeller, Table of n, a(n) for n = 1..11000

Cf. A031298.

a068505 n = foldr (\d v -> v * b + d) 0 dds where
b = maximum dds + 1
dds = a031298_row n
-- Reinhard Zumkeller, Feb 17 2013, Dec 29 2011

f:= proc(n) local b,L,i;
L:= convert(n,base,10);
b:= max(L);
add(L[i]*(b+1)^(i-1),i=1..nops(L));
end proc:
map(f, [$1..100]); # Robert Israel, Feb 02 2016

a[n_] := (id = IntegerDigits[n] // Reverse; b = Max[id]+1; id.b^Range[0, Length[id]-1]); Table[a[n], {n, 1, 75}] (* Jean-François Alcover, May 15 2013 *)
Table[FromDigits[IntegerDigits[n],Max[IntegerDigits[n]+1]],{n,80}] (* Harvey P. Dale, Dec 02 2015 *)

a(n)=my(d = digits(n), b = vecmax(d)); subst(Pol(d), x, b+1); \\ Michel Marcus, Feb 12 2016

Definition clarified and comment corrected by Martin Büttner, Feb 02 2016

A354760 a(0) = 0; for n >= 1, a(n) = a(n - A054055(n)) + 1.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13

Offset: 0

Ctibor O. Zizka, Jun 06 2022

Number of steps needed to reach zero when starting from k = n and repeatedly applying the map that replaces k by k - A054055(k). a(n) ~ n/ln(n).

			n = 12, a(12) = 1 + a(12 - A054055(12)) = 1 + a(10) = 1 + 1 + a(10 - A054055(10)) = 2 + a(9) = 2 + 1 + a(9 - A054055(9)) = 2 + 1 + 0 = 3.

Cf. A054055.

a[0] = 0; a[n_] := a[n] = a[n - Max[IntegerDigits[n]]] + 1; Array[a, 100, 0] (* Amiram Eldar, Jun 06 2022 *)

A007088 The binary numbers (or binary words, or binary vectors, or binary expansion of n): numbers written in base 2.

Original entry on oeis.org

0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 10000, 10001, 10010, 10011, 10100, 10101, 10110, 10111, 11000, 11001, 11010, 11011, 11100, 11101, 11110, 11111, 100000, 100001, 100010, 100011, 100100, 100101, 100110, 100111

Offset: 0

N. J. A. Sloane, Robert G. Wilson v

List of binary numbers. (This comment is to assist people searching for that particular phrase. - N. J. A. Sloane, Apr 08 2016)
Or, numbers that are sums of distinct powers of 10.
Or, numbers having only digits 0 and 1 in their decimal representation.
Complement of A136399; A064770(a(n)) = a(n). - Reinhard Zumkeller, Dec 30 2007
From Rick L. Shepherd, Jun 25 2009: (Start)
Nonnegative integers with no decimal digit > 1.
Thus nonnegative integers n in base 10 such that kn can be calculated by normal addition (i.e., n + n + ... + n, with k n's (but not necessarily k + k + ... + k, with n k's)) or multiplication without requiring any carry operations for 0 <= k <= 9. (End)
For n > 1: A257773(a(n)) = 10, numbers that are Belgian-k for k=0..9. - Reinhard Zumkeller, May 08 2015
For any integer n>=0, find the binary representation and then interpret as decimal representation giving a(n). - Michael Somos, Nov 15 2015
N is in this sequence iff A007953(N) = A101337(N). A028897 is a left inverse. - M. F. Hasler, Nov 18 2019
For n > 0, numbers whose largest decimal digit is 1. - Stefano Spezia, Nov 15 2023

			a(6)=110 because (1/2)*((1-(-1)^6)*10^0 + (1-(-1)^3)*10^1 + (1-(-1)^1)*10^2) = 10 + 100.
G.f. = x + 10*x^2 + 11*x^3 + 100*x^4 + 101*x^5 + 110*x^6 + 111*x^7 + 1000*x^8 + ...
.
  000    The numbers < 2^n can be regarded as vectors with
  001    a fixed length n if padded with zeros on the left
  010    side. This represents the n-fold Cartesian product
  011    over the set {0, 1}. In the example on the left,
  100    n = 3. (See also the second Python program.)
  101    Binary vectors in this format can also be seen as a
  110    representation of the subsets of a set with n elements.
  111    - _Peter Luschny_, Jan 22 2024

John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See p. 21.
Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §2.8 Binary, Octal, Hexadecimal, p. 64.
Manfred R. Schroeder, "Fractals, Chaos, Power Laws", W. H. Freeman, 1991, p. 383.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, Table of n, a(n) for n = 0..32768 (first 8192 terms from Franklin T. Adams-Watters)
Heinz Gumin, Herrn von Leibniz' Rechnung mit Null und Eins, Siemens AG, 3. Auflage 1979 -- contains facsimiles of Leibniz's papers from 1679 and 1703.
Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, p. 45.
G. W. Leibniz, Explication de l'arithmétique binaire, qui se sert des seuls caractères 0 & 1; avec des remarques sur son utilité, et sur ce qu'elle donne le sens des anciennes figures chinoises de Fohy, Mémoires de l'Académie Royale des Sciences, 1703, pp. 85-89; reprinted in Gumin (1979).
N. J. A. Sloane, Table of a(n) for n = 0..1048576 (A large file).
Robert G. Wilson v, Letter to N. J. A. Sloane, Sep. 1992.
Index entries for sequences related to Most Wanted Primes video.
Index entries for 10-automatic sequences.
Index entries for sequences related to binary expansion of n.

The basic sequences concerning the binary expansion of n are this one, A000120 (Hammingweight: sum of bits), A000788 (partial sums of A000120), A000069 (A000120 is odd), A001969 (A000120 is even), A023416 (number of bits 0), A059015 (partial sums). Bisections A099820 and A099821.
Cf. A028897 (convert binary to decimal).
Cf. A000042, A007089-A007095, A000695, A005836, A033042-A033052, A159918, A004290, A169965, A169966, A169967, A169964, A204093, A204094, A204095, A097256, A257773, A257770.
Cf. A000290, A001737, A007953, A030308, A054055, A064770, A101337, A136399.

a007088 0 = 0
a007088 n = 10 * a007088 n' + m where (n',m) = divMod n 2
-- Reinhard Zumkeller, Jan 10 2012

A007088 := n-> convert(n, binary): seq(A007088(n), n=0..50); # R. J. Mathar, Aug 11 2009

Table[ FromDigits[ IntegerDigits[n, 2]], {n, 0, 39}]
Table[Sum[ (Floor[( Mod[f/2 ^n, 2])])*(10^n) , {n, 0, Floor[Log[2, f]]}], {f, 1, 100}] (* José de Jesús Camacho Medina, Jul 24 2014 *)
FromDigits/@Tuples[{1,0},6]//Sort (* Harvey P. Dale, Aug 10 2017 *)

{a(n) = subst( Pol( binary(n)), x, 10)}; /* Michael Somos, Jun 07 2002 */

{a(n) = if( n<=0, 0, n%2 + 10*a(n\2))}; /* Michael Somos, Jun 07 2002 */

a(n)=fromdigits(binary(n),10) \\ Charles R Greathouse IV, Apr 08 2015

def a(n): return int(bin(n)[2:])
print([a(n) for n in range(40)]) # Michael S. Branicky, Jan 10 2021

from itertools import product
n = 4
for p in product([0, 1], repeat=n): print(''.join(str(x) for x in p))
# Peter Luschny, Jan 22 2024

a(n) = Sum_{i=0..m} d(i)*10^i, where Sum_{i=0..m} d(i)*2^i is the base 2 representation of n.
a(n) = (1/2)*Sum_{i>=0} (1-(-1)^floor(n/2^i))*10^i. - Benoit Cloitre, Nov 20 2001
a(n) = A097256(n)/9.
a(2n) = 10*a(n), a(2n+1) = a(2n)+1.
G.f.: 1/(1-x) * Sum_{k>=0} 10^k * x^(2^k)/(1+x^(2^k)) - for sequence as decimal integers. - Franklin T. Adams-Watters, Jun 16 2006
a(A000290(n)) = A001737(n). - Reinhard Zumkeller, Apr 25 2009
a(n) = Sum_{k>=0} A030308(n,k)*10^k. - Philippe Deléham, Oct 19 2011
For n > 0: A054055(a(n)) = 1. - Reinhard Zumkeller, Apr 25 2012
a(n) = Sum_{k=0..floor(log_2(n))} floor((Mod(n/2^k, 2)))*(10^k). - José de Jesús Camacho Medina, Jul 24 2014

A054054 Smallest digit of n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 2, 3, 3, 3, 3, 3, 3, 3, 0, 1, 2, 3, 4, 4, 4, 4, 4, 4, 0, 1, 2, 3, 4, 5, 5, 5, 5, 5, 0, 1, 2, 3, 4, 5, 6, 6, 6, 6, 0, 1, 2, 3, 4, 5, 6, 7, 7, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 0, 0, 0

Offset: 0

Henry Bottomley, Apr 29 2000

a(n) = 0 for almost all n. - Charles R Greathouse IV, Oct 02 2013

More precisely, a(n) = 0 asymptotically almost surely, i.e., except for a set of density 0: As the number of digits of n grows, the probability of having no zero digit goes to zero as 0.9^(length of n), although there are infinitely many counterexamples. - M. F. Hasler, Oct 11 2015

			a(12) = 1 because 1 < 2.

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

Cf. A054055.

Cf. A061601, A011540, A052382, A262188.

a054054 = f 9 where
   f m x | x <= 9 = min m x
         | otherwise = f (min m d) x' where (x',d) = divMod x 10
-- Reinhard Zumkeller, Jun 20 2012, Apr 25 2012

seq(min(convert(n,base,10)),n=0..100); # Robert Israel, Jul 07 2016

Mathematica
```
A054054[n_]:=Min[IntegerDigits[n]]
```

A054054(n)=if(n,vecmin(digits(n)))  \\ or: Set(digits(n))[1]. - M. F. Hasler, Jan 23 2013

a(A011540(n)) = 0; a(A052382(n)) > 0. - Reinhard Zumkeller, Apr 25 2012
a(n) = A262188(n,0). - Reinhard Zumkeller, Sep 14 2015
a(n) = 0 iff A007954(n) = 0. - M. F. Hasler, Oct 11 2015
a(n) = 9 - A054055(A061601(n)). - Robert Israel, Jul 07 2016

Edited by M. F. Hasler, Oct 11 2015

A037904 Greatest digit of n - least digit of n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 9

Offset: 1

Clark Kimberling

a(n) = A054055(n)-A054054(n); a(A010785(n)) = 0; for k>0: a(n) = a(n*10^k + A000030(n)) = a(n*10^k + A010879(n)) = a(n*10^k + A054054(n)) = a(n*10^k + A054055(n)) . - Reinhard Zumkeller, Dec 14 2007; corrected by David Wasserman, May 21 2008

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

Cf. A040163, A064834.

a037904 = f 9 0 where
   f u v 0 = v - u
   f u v z = f (min u d) (max v d) z' where (z', d) = divMod z 10
-- Reinhard Zumkeller, Dec 16 2013

f:= n -> (max-min)(convert(n,base,10)):
map(f, [$1..1000]); # Robert Israel, Jul 07 2016

f[n_] := Block[{d = IntegerDigits[n]}, Max[d] - Min[d]]; Table[ f[n], {n, 1, 15}]

a(n)=my(d=digits(n)); vecmax(d)-vecmin(d) \\ Charles R Greathouse IV, Feb 07 2017

def A037904(n): return int(max(s:=str(n)))-int(min(s)) # Chai Wah Wu, Nov 10 2023

Incorrect comments deleted by Robert Israel, Jul 07 2016

A083890 Number of divisors of n with largest digit = 3 (base 10).

Original entry on oeis.org

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

Offset: 1

Reinhard Zumkeller, May 08 2003

			n=132, 3 of the 12 divisors of 132 have largest digit =3: {3,33,132}, therefore a(132)=3.

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

Cf. A054055, A000005, A083898, A083888, A083889, A083891, A083892, A083893, A083894, A083895, A083896, A277965.

[#[d:d in Divisors(n) | Max(Intseq(d)) eq 3]: n in [1..130]]; // Marius A. Burtea, Oct 06 2019

f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:
d:= 3:
map(f, [$1..200]); # Robert Israel, Oct 06 2019

With[{k = 3}, Array[DivisorSum[#, 1 &, And[#[[k]] > 0, Total@ #[[k + 1 ;; 9]] == 0] &@ DigitCount[#] &] &, 105]] (* Michael De Vlieger, Oct 06 2019 *)
Table[Count[Divisors[n],?(Max[IntegerDigits[#]]==3&)],{n,120}] (* _Harvey P. Dale, Sep 05 2020 *)

a(n) = A000005(n) - A083888(n) - A083889(n) - A083891(n) - A083892(n) - A083893(n) - A083894(n) - A083895(n) - A083896(n) = A083898(n) - A083897(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A277965(k) = 0.84217457724798904648... . - Amiram Eldar, Jan 04 2024

A083891 Number of divisors of n with largest digit = 4 (base 10).

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 1, 2, 1, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0

Offset: 1

Reinhard Zumkeller, May 08 2003

			n=120, 3 of the 16 divisors of 120 have largest digit=4: {4,24,40}, therefore a(120)=3.

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

Cf. A054055, A000005, A083899, A277966.

ld4:= n -> max(convert(n,base,10)) = 4:
f:= n -> nops(select(ld4,numtheory:-divisors(n))):
map(f, [$1..100]); # Robert Israel, May 02 2019

Table[Count[Divisors[n],?(Max[IntegerDigits[#]]==4&)],{n,110}] (* _Harvey P. Dale, Feb 19 2016 *)

a(n) = A000005(n) - A083888(n) - A083889(n) - A083890(n) - A083892(n) - A083893(n) - A083894(n) - A083895(n) - A083896(n) = A083899(n) - A083898(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A277966(k) = 0.98827280431174433126... . - Amiram Eldar, Jan 04 2024

A083892 Number of divisors of n with largest digit = 5 (base 10).

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 1, 1, 1, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 1, 0, 1, 4

Offset: 1

Reinhard Zumkeller, May 08 2003

			n=125, 3 of the 4 divisors of 125 have largest digit =5: {5,25,125}, therefore a(125)=3.

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

Cf. A054055, A000005, A083900, A083888, A083889, A083890, A083891, A083893, A083894, A083895, A083896, A283608.

f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:
d:= 5:
map(f, [$1..200]); # Robert Israel, Oct 06 2019

Table[Count[Divisors[n],?(Max[IntegerDigits[#]]==5&)],{n,110}] (* _Harvey P. Dale, Aug 08 2015 *)

a(n) = A000005(n) - A083888(n) - A083889(n) - A083890(n) - A083891(n) - A083893(n) - A083894(n) - A083895(n) - A083896(n) = A083900(n) - A083899(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A283608(k) = 1.32926350368137107677... . - Amiram Eldar, Jan 04 2024

A083893 Number of divisors of n with largest digit = 6 (base 10).

Original entry on oeis.org

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

Offset: 1

Reinhard Zumkeller, May 08 2003

			n=240, 3 of the 20 divisors of 240 have largest digit =6: {6,16,60}, therefore a(240)=3.

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

Cf. A054055, A000005, A083901, A083888, A083889, A083890, A083891, A083892, A083894, A083895, A083896, A283609.

[#[d:d in Divisors(n) | Max(Intseq(d)) eq 6]: n in [1..150]]; // Marius A. Burtea, Oct 06 2019

f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:
d:= 6:
map(f, [$1..200]); # Robert Israel, Oct 06 2019

With[{k = 6}, Array[DivisorSum[#, 1 &, And[#[[k]] > 0, Total@ #[[k + 1 ;; 9]] == 0] &@ DigitCount[#] &] &, 105]] (* Michael De Vlieger, Oct 06 2019 *)

a(n) = A000005(n) - A083888(n) - A083889(n) - A083890(n) - A083891(n) - A083892(n) - A083894(n) - A083895(n) - A083896(n) = A083901(n) - A083900(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A283609(k) = 2.06890539387954414920... . - Amiram Eldar, Jan 04 2024

A083894 Number of divisors of n with largest digit = 7 (base 10).

Original entry on oeis.org

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

Offset: 1

Reinhard Zumkeller, May 08 2003

			n=119, 2 of the 4 divisors of 119 have largest digit =7: {7,17}, therefore a(119)=2.

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

Cf. A054055, A000005, A083902, A083888, A083889, A083890, A083891, A083892, A083893, A083895, A083896, A283610.

f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:
d:= 7:
map(f, [$1..200]); # Robert Israel, Oct 06 2019

Table[Count[Divisors[n],?(Max[IntegerDigits[#]]==7&)],{n,120}] (* _Harvey P. Dale, Oct 16 2021 *)

a(n) = A000005(n) - A083888(n) - A083889(n) - A083890(n) - A083891(n) - A083892(n) - A083893(n) - A083895(n) - A083896(n) = A083902(n) - A083901(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A283610(k) = 3.96819589328234218540... . - Amiram Eldar, Jan 04 2024

cp's OEIS Frontend

A068505 Decimal representation of n interpreted in base b+1, where b=A054055(n) is the largest digit in decimal representation of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

Extensions

A354760 a(0) = 0; for n >= 1, a(n) = a(n - A054055(n)) + 1.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A007088 The binary numbers (or binary words, or binary vectors, or binary expansion of n): numbers written in base 2.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

PARI

PARI

Python

Python

Formula

A054054 Smallest digit of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

Formula

Extensions

A037904 Greatest digit of n - least digit of n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

Python

Extensions

A083890 Number of divisors of n with largest digit = 3 (base 10).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs