A122840 -id:A122840 - cp's OEIS frontend

A102671 Number of digits >= 3 in decimal representation of n.

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

Offset: 0

N. J. A. Sloane, Feb 03 2005

a(n) = 0 iff n is in A007089 (numbers in base 3). - Bernard Schott, Nov 20 2022

Hieronymus Fischer, Table of n, a(n) for n = 0..10000

Cf. A007089, A027868, A054899, A055640, A055641, A102669-A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564. Partial sums see A102672.

Cf. A000120, A000788, A023416, A059015 (for base 2).

p:=proc(n) local b,ct,j: b:=convert(n,base,10): ct:=0: for j from 1 to nops(b) do if b[j]>=3 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(p(n),n=0..116); # Emeric Deutsch, Feb 23 2005

Table[Count[IntegerDigits[n],?(#>2&)],{n,0,110}] (* _Harvey P. Dale, Mar 07 2012 *)

From Hieronymus Fischer, Jun 10 2012: (Start)
a(n) = Sum_{j=1..m+1} (floor((n/10^j) + 7/10) - floor(n/10^j)), where m = floor(log_10(n)).
G.f.: g(x) = (1/(1-x))*Sum_{j>=0} (x^(3*10^j) - x^(10*10^j))/(1 - x^10^(j+1)). (End)

More terms from Emeric Deutsch, Feb 23 2005

A102672 Number of digits >= 3 in the decimal representations of all integers from 0 to n.

Original entry on oeis.org

0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 7, 7, 7, 8, 9, 10, 11, 12, 13, 14, 14, 14, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 28, 30, 32, 34, 36, 38, 39, 40, 41, 43, 45, 47, 49, 51, 53, 55, 56, 57, 58, 60, 62, 64, 66, 68, 70, 72, 73, 74, 75, 77, 79, 81, 83, 85, 87, 89, 90, 91, 92, 94

Offset: 0

N. J. A. Sloane, Feb 03 2005

The total number of digits >= 3 occurring in all the numbers 0, 1, 2, ... n (in decimal representation). - Hieronymus Fischer, Jun 10 2012

Hieronymus Fischer, Table of n, a(n) for n = 0..10000

Partial sums of A102671.
Cf. A027868, A054899, A055640, A055641, A102669-A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564. Partial sums of A102671.
Cf. A000120, A000788, A023416, A059015 (for base 2).

p:=proc(n) local b,ct,j: b:=convert(n,base,10): ct:=0: for j from 1 to nops(b) do if b[j]>=3 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(add(p(i),i=0..n), n=0..80); # Emeric Deutsch, Feb 23 2005

Accumulate[Table[Count[IntegerDigits[n],?(#>2&)],{n,0,80}]] (* _Harvey P. Dale, Nov 23 2014 *)

From Hieronymus Fischer, Jun 10 2012: (Start)
a(n) = (1/2)*Sum_{j=1..m+1} (floor(n/10^j + 7/10)*(2n + 2 + (2/5 - floor(n/10^j + 7/10))*10^j) - floor(n/10^j)*(2n + 2 - (1 + floor(n/10^j)) * 10^j)), where m = floor(log_10(n)).
a(n) = (n+1)*A102671(n) + (1/2)*Sum_{j=1..m+1} (((2/5)*floor(n/10^j + 7/10) + floor(n/10^j))*10^j - (floor(n/10^j + 7/10)^2 - floor(n/10^j)^2)*10^j), where m = floor(log_10(n)).
a(10^m - 1) = 7*m*10^(m-1).
(This is the total number of digits >= 3 occurring in all the numbers with <= m places.)
G.f.: g(x) = (1/(1-x)^2)*Sum_{j>=0} (x^(3*10^j) - x^(10*10^j))/(1 - x^10^(j+1)). (End)

More terms from Emeric Deutsch, Feb 23 2005

A102673 Number of digits >= 4 in decimal representation of n.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Feb 03 2005

a(n) = 0 iff n is in A007090 (numbers in base 4). - Bernard Schott, Feb 01 2023

Hieronymus Fischer, Table of n, a(n) for n = 0..10000

Cf. A027868, A054899, A055640, A055641, A102669-A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564. Partial sums see A102674.

Cf. A000120, A000788, A007090, A023416, A059015 (for base 2).

p:=proc(n) local b,ct,j: b:=convert(n,base,10): ct:=0: for j from 1 to nops(b) do if b[j]>=4 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(p(n),n=0..125); # Emeric Deutsch, Feb 22 2005

Table[Total@ Take[DigitCount@ n, {4, 9}], {n, 0, 104}] (* Michael De Vlieger, Aug 17 2017 *)

From Hieronymus Fischer, Jun 10 2012: (Start)
a(n) = Sum_{j=1..m+1} (floor(n/10^j + 3/5) - floor(n/10^j)), where m = floor(log_10(n)).
G.f.: g(x) = (1/(1-x))*Sum_{j>=0} (x^(4*10^j) - x^(10*10^j))/(1 - x^10^(j+1)). (End)

More terms from Emeric Deutsch, Feb 22 2005

A102674 Number of digits >= 4 in the decimal representations of all integers from 0 to n.

Original entry on oeis.org

0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 6, 6, 6, 6, 7, 8, 9, 10, 11, 12, 12, 12, 12, 12, 13, 14, 15, 16, 17, 18, 18, 18, 18, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 32, 34, 36, 38, 40, 41, 42, 43, 44, 46, 48, 50, 52, 54, 56, 57, 58, 59, 60, 62, 64, 66, 68, 70, 72, 73, 74, 75, 76, 78

Offset: 0

N. J. A. Sloane, Feb 03 2005

The total number of digits >= 4 occurring in all the numbers 0, 1, 2, ... n (in decimal representation). - Hieronymus Fischer, Jun 10 2012

Hieronymus Fischer, Table of n, a(n) for n = 0..10000

Partial sums of A102673.
Cf. A027868, A054899, A055640, A055641, A102669-A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564.
Cf. A000120, A000788, A023416, A059015 (for base 2).

p:=proc(n) local b,ct,j: b:=convert(n,base,10): ct:=0: for j from 1 to nops(b) do if b[j]>=4 then ct:=ct+1 else ct:=ct fi od: ct: end:seq(add(p(i),i=0..n),n=0..90); # Emeric Deutsch, Feb 22 2005

Accumulate[Table[Total[Drop[Most[DigitCount[n]],3]],{n,0,80}]] (* Harvey P. Dale, Nov 27 2015 *)

From Hieronymus Fischer, Jun 10 2012: (Start)
a(n) = (1/2)*Sum_{j=1..m+1} (floor(n/10^j + 3/5)*(2n + 2 + (1/5 - floor(n/10^j + 3/5))*10^j) - floor(n/10^j)*(2n + 2 - (1 + floor(n/10^j)) * 10^j)), where m = floor(log_10(n)).
a(n) = (n+1)*A102673(n) + (1/2)*Sum_{j=1..m+1} (((1/5)*floor(n/10^j + 3/5) + floor(n/10^j))*10^j - (floor(n/10^j + 3/5)^2 - floor(n/10^j)^2)*10^j), where m = floor(log_10(n)).
a(10^m - 1) = 6*m*10^(m-1).
(This is the total number of digits >= 4 occurring in all the numbers with <= m places.)
G.f.: g(x) = (1/(1-x)^2)*Sum_{j>=0} (x^(4*10^j) - x^(10*10^j))/(1 - x^10^(j+1)). (End)

More terms from Emeric Deutsch, Feb 22 2005

A102675 Number of digits >= 5 in decimal representation of n.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Feb 03 2005

a(n) = 0 iff n is in A007091 (numbers in base 5). - Bernard Schott, Feb 02 2023

Curtis Cooper, Number of large digits in the positive integers not exceeding n, Abstracts Amer. Math. Soc., 25 (No. 1, 2004), p. 38, Abstract 993-11-964.

Hieronymus Fischer, Table of n, a(n) for n = 0..10000

Cf. A007091 (indices of 0's), A027868, A054899, A055640, A055641, A102669-A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564, A102676 (partial sums).

Cf. A000120, A000788, A023416, A059015 (for base 2).

p:=proc(n) local b,ct,j: b:=convert(n,base,10): ct:=0: for j from 1 to nops(b) do if b[j]>=5 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(p(n),n=0..120); # Emeric Deutsch, Feb 23 2005

Table[Count[IntegerDigits[n],?(#>4&)],{n,0,120}] (* _Harvey P. Dale, Nov 13 2013 *)

From Hieronymus Fischer, Jun 10 2012: (Start)
a(n) = Sum_{j=1..m+1} (floor(n/10^j + 1/2) - floor(n/10^j)), where m = floor(log_10(n)).
G.f.: g(x) = (1/(1-x))*Sum_{j>=0} (x^(5*10^j) - x^(10*10^j))/(1 - x^10^(j+1)).
G.f.: g(x) = (1/(1-x))*Sum_{j>=0} x^(5*10^j)/(1 + x^(5*10^j)).  (End)

More terms from Emeric Deutsch, Feb 23 2005

A102676 Number of digits >= 5 in the decimal representations of all integers from 0 to n.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 10, 11, 12, 13, 14, 15, 15, 15, 15, 15, 15, 16, 17, 18, 19, 20, 20, 20, 20, 20, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 34, 36, 38, 40, 41, 42, 43, 44, 45, 47, 49, 51, 53, 55, 56, 57, 58, 59, 60, 62

Offset: 0

N. J. A. Sloane, Feb 03 2005

The total number of digits >= 5 occurring in all the numbers 0, 1, 2, ... n (in decimal representation). - Hieronymus Fischer, Jun 10 2012

Curtis Cooper, Number of large digits in the positive integers not exceeding n, Abstracts Amer. Math. Soc., 25 (No. 1, 2004), p. 38, Abstract 993-11-964.

Hieronymus Fischer, Table of n, a(n) for n = 0..10000

Partial sums of A102675.
Cf. A027868, A054899, A055640, A055641, A102669-A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564.
Cf. A000120, A000788, A023416, A059015 (for base 2).

p:=proc(n) local b,ct,j: b:=convert(n,base,10): ct:=0: for j from 1 to nops(b) do if b[j]>=5 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(add(p(i),i=0..n), n=0..83); # Emeric Deutsch, Feb 23 2005

Accumulate[Table[Total[Take[DigitCount[n],{5,9}]],{n,0,80}]] (* Harvey P. Dale, Apr 27 2015 *)

From Hieronymus Fischer, Jun 10 2012: (Start)
a(n) = (1/2)*Sum_{j=1..m+1} (floor(n/10^j + 1/2)*(2n + 2 - floor(n/10^j + 1/2)*10^j - floor(n/10^j)*(2n + 2 - (1+floor(n/10^j))*10^j)), where m = floor(log_10(n)).
a(n) = (n+1)*A102675(n) + (1/2)*Sum_{j=1..m+1} (floor(n/10^j)*10^j - (floor(n/10^j + 1/2)^2 - floor(n/10^j)^2)*10^j), where m = floor(log_10(n)).
a(10^m-1) = 5*m*10^(m-1).
(This is the total number of digits >= 5 occurring in all the numbers with <= m places.)
G.f.: g(x) = (1/(1-x)^2)*Sum_{j>=0} (x^(5*10^j) - x^(10*10^j))/(1-x^10^(j+1)).
G.f.: g(x) = (1/(1-x)^2)*Sum_{j>=0} x^(5*10^j)/(1+x^(5*10^j)).  (End)

More terms from Emeric Deutsch, Feb 23 2005

A102678 Number of digits >= 6 in the decimal representations of all integers from 0 to n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 4, 4, 4, 4, 4, 4, 5, 6, 7, 8, 8, 8, 8, 8, 8, 8, 9, 10, 11, 12, 12, 12, 12, 12, 12, 12, 13, 14, 15, 16, 16, 16, 16, 16, 16, 16, 17, 18, 19, 20, 20, 20, 20, 20, 20, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 34, 36, 38, 39, 40, 41, 42, 43, 44, 46, 48

Offset: 0

N. J. A. Sloane, Feb 03 2005

The total number of digits >= 6 occurring in all the numbers 0, 1, 2, ... n (in decimal representation). - Hieronymus Fischer, Jun 10 2012

Hieronymus Fischer, Table of n, a(n) for n = 0..10000

Partial sums of A102677.
Cf. A027868, A054899, A055640, A055641, A102669-A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564. Partial sums of A102669.
Cf. A000120, A000788, A023416, A059015 (for base 2).

p:=proc(n) local b,ct,j: b:=convert(n,base,10): ct:=0: for j from 1 to nops(b) do if b[j]>=6 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(add(p(i),i=0..n), n=0..86); # Emeric Deutsch, Feb 23 2005

From Hieronymus Fischer, Jun 10 2012: (Start)
a(n) = (1/2)*Sum_{j=1..m+1} (floor(n/10^j + 2/5)*(2n + 2 - (1/5 + floor(n/10^j + 2/5))*10^j) - floor(n/10^j)*(2n + 2 - (1+floor(n/10^j)) * 10^j)), where m = floor(log_10(n)).
a(n) = (n+1)*A102677(n) + (1/2)*Sum_{j=1..m+1} ((-1/5*floor(n/10^j + 2/5) + floor(n/10^j))*10^j - (floor(n/10^j + 2/5)^2 - floor(n/10^j)^2)*10^j), where m = floor(log_10(n)).
a(10^m-1) = 4*m*10^(m-1).
(this is total number of digits >= 6 occurring in all the numbers with <= m places).
G.f.: g(x) = (1/(1-x)^2)*Sum_{j>=0} (x^(6*10^j) - x^(10*10^j))/(1 - x^10^(j+1)). (End)

More terms from Emeric Deutsch, Feb 23 2005

An incorrect g.f. was deleted by N. J. A. Sloane, Sep 16 2009

A102680 Number of digits >= 7 in the decimal representations of all integers from 0 to n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 32, 34, 35, 36

Offset: 0

N. J. A. Sloane, Feb 03 2005

The total number of digits >= 7 occurring in all the numbers 0, 1, 2, ..., n (in decimal representation). - Hieronymus Fischer, Jun 10 2012

Hieronymus Fischer, Table of n, a(n) for n = 0..10000

Partial sums of A102679.
Cf. A027868, A054899, A055640, A055641, A102669-A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564. Partial sums of A102669.
Cf. A000120, A000788, A023416, A059015 (for base 2).

p:=proc(n) local b,ct,j: b:=convert(n,base,10): ct:=0: for j from 1 to nops(b) do if b[j]>=7 then ct:=ct+1 else ct:=ct fi od: ct: end:
seq(add(p(i),i=0..n), n=0..90);
# Emeric Deutsch

Accumulate[Table[Count[IntegerDigits[n],?(#>6&)],{n,0,90}]] (* _Harvey P. Dale, Sep 04 2018 *)

From Hieronymus Fischer, Jun 10 2012: (Start)
a(n) = (1/2)*Sum_{j=1..m+1} (floor(n/10^j + 7/10)*(2n + 2 - (2/5 + floor(n/10^j + 7/10))*10^j) - floor(n/10^j)*(2n + 2 - (1+floor(n/10^j)) * 10^j)), where m=floor(log_10(n)).
a(n) = (n+1)*A102679(n) + (1/2)*Sum_{j=1..m+1} (((-2/5)*floor(n/10^j + 7/10) + floor(n/10^j))*10^j - (floor(n/10^j + 7/10)^2 - floor(n/10^j)^2)*10^j), where m=floor(log_10(n)).
a(10^m-1) = 3*m*10^(m-1).
(this is total number of digits >= 7 occurring in all the numbers with <= m places).
G.f.: g(x) = (1/(1-x)^2)*Sum_{j>=0} (x^(7*10^j) - x^(10*10^j))/(1-x^10^(j+1)). (End)

More terms from Emeric Deutsch, Feb 23 2005

A102682 Number of digits >= 8 in the decimal representations of all integers from 0 to n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 16, 17, 18, 19, 20, 21, 22

Offset: 0

N. J. A. Sloane, Feb 03 2005

The total number of digits >= 8 occurring in all the numbers 0, 1, 2, ... n (in decimal representation). - Hieronymus Fischer, Jun 10 2012

Hieronymus Fischer, Table of n, a(n) for n = 0..10000

Partial sums of A102681.
Cf. A027868, A054899, A055640, A055641, A102669-A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564.
Cf. A000120, A000788, A023416, A059015 (for base 2).

p:=proc(n) local b,ct,j: b:=convert(n,base,10): ct:=0: for j from 1 to nops(b) do if b[j]>=8 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(add(p(i),i=0..n), n=0..95); # Emeric Deutsch, Feb 23 2005

From Hieronymus Fischer, Jun 10 2012: (Start)
a(n) = (1/2)*Sum_{j=1..m+1} (floor(n/10^j + 1/5)*(2n + 2 - (3/5 + floor(n/10^j + 1/5))*10^j) - floor(n/10^j)*(2n + 2 - (1+floor(n/10^j)) * 10^j)), where m = floor(log_10(n)).
a(n) = (n+1)*A102681(n) + (1/2)*Sum_{j=1..m+1} ((-3/5*floor(n/10^j + 1/5) + floor(n/10^j))*10^j - (floor(n/10^j + 1/5)^2 - floor(n/10^j)^2)*10^j), where m = floor(log_10(n)).
a(10^m-1) = 2*m*10^(m-1). (this is total number of digits >= 8 occurring in all the numbers with <= m places).
G.f.: g(x) = (1/(1-x)^2)*Sum_{j>=0} (x^(8*10^j) - x^(10*10^j))/(1-x^10^(j+1)). (End)

More terms from Emeric Deutsch, Feb 23 2005

An incorrect g.f. was deleted by N. J. A. Sloane, Sep 16 2009

A369860 The orbit of n under iterations of x -> c(x)10^L(x-c(x)) + x-c(x), where c(x) = floor(x^(1/3))^3, L(x) = floor(log_10(max(x,1))+1), enters a pseudo-loop x(k) = a^3 10^((k-k0)*L(b)) + b beyond some k0. This sequence lists the a-values.

Original entry on oeis.org

18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 883, 883, 883, 883, 883, 883, 883, 883, 883, 581, 581, 581, 581, 581, 581, 581, 581, 581, 581, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 8, 8, 8, 8

Offset: 1

M. F. Hasler, Apr 05 2024

The iterated function can also be defined as x -> concatenate(c(x), x-c(x)), where c = A048762 gives the largest perfect cube <= x and x - c(x) = A055400(x) is the "cube excess" of x. L = A055642 gives the number of decimal digits.

The corresponding b-values are listed in A369861.

			Starting with 1, we get 1 -> 10 -> 82 (since 8 is the largest cube <= 10, at distance 2) -> 6418 (since the cube 64 is at distance 18) -> 5832586 (since 5832 = 18^3 is at distance 586) -> 5832000586 (since 180^3 is again at distance 586) -> ...: Each time 3 '0's will be inserted in front of the remainder which remains always the same, as does the cube root a(1) = 18, up to factors of 10.
Starting with 2, we get 2 -> 11 (since the largest cube <= 2 is 1, at distance 1) -> 83 (since largest cube <= 11 is 8, at distance 2) -> 6419 (since the cube 64 is at distance 19) -> 5832587 (since 5832 = 18^3 is at distance 587). We see that in this sequence each term is just one more than that of the preceding sequence, so the cube root remains the same, a(2) = a(1) = 18.
For n = 18, we get 18 -> 810 (since the largest cube <= 18 is 8, at distance 10) -> 72981 (since the cube 729 is at distance 81) -> 689214060 (since 68921 = 41^3 is at distance 4060) -> 688465387748673 (since 688465387 = 883^3 is at distance 748673), from where on the cube root a(18) = 883 gets an additional factor 10 at each step, but the cube excess A055400 remains the same, A369861(18) = 748673.
See A369861 for more examples.

Eric Angelini, Pseudo-loops with cubes, and post to math-fun discussion list; April 1, 2024

Cf. A000578 (cubes), A048766 (cube root), A048762 (largest cube <= n), A055400 (cube excess), A055642 (length of n in base 10), A122840 (10-valuation of n).

Cf. A369861 (b-values).

A369860(n)={until(, my(c=sqrtnint(n, 3), v=valuation(c, 10), L=logint(max(n-c^3, 1), 10)+1); L==v*3 && return(c/10^v); n += c^3*(10^L-1))}

import sympy # for integer_nthroot (A048766), multiplicity (A122840)
def A369860(n: int):
    while True:
        C = sympy.integer_nthroot(n, 3)[0]; L = A055642(n-C**3)
        if sympy.multiplicity(10, C)*3 == L: return C//10**(L//3)
        n += C**3 * (10**L - 1)

cp's OEIS Frontend

A102671 Number of digits >= 3 in decimal representation of n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A102672 Number of digits >= 3 in the decimal representations of all integers from 0 to n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A102673 Number of digits >= 4 in decimal representation of n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A102674 Number of digits >= 4 in the decimal representations of all integers from 0 to n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A102675 Number of digits >= 5 in decimal representation of n.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A102676 Number of digits >= 5 in the decimal representations of all integers from 0 to n.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A102678 Number of digits >= 6 in the decimal representations of all integers from 0 to n.

Views

Author

Keywords

Comments

A369860 The orbit of n under iterations of x -> c(x)10^L(x-c(x)) + x-c(x), where c(x) = floor(x^(1/3))^3, L(x) = floor(log_10(max(x,1))+1), enters a pseudo-loop x(k) = a^3 10^((k-k0)*L(b)) + b beyond some k0. This sequence lists the a-values.