A052386 -id:A052386 - cp's OEIS frontend

A091634 Number of primes less than 10^n which do not contain the digit 0.

4, 25, 153, 1010, 7122, 52313, 397866, 3103348, 24649318, 198536215, 1616808581, 13287264748, 110033428309, 917072930187

Offset: 1

Enoch Haga, Jan 30 2004

			a(3) = 153 because there are 168 primes less than 10^3, 15 primes have at least one zero; 168 - 15 = 153.

a(n) + A091644(n) = A006880(n).

Cf. A091635, A091636, A091637, A091638, A091639, A091640, A091641, A091642, A091643.

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; c = 0; p = 1; Do[ While[ p = NextPrim[p]; p < 10^n, If[ Position[ IntegerDigits[p], 0] == {}, c++ ]]; Print[c]; p--, {n, 1, 8}] (* Robert G. Wilson v, Feb 02 2004 *)
Table[PrimePi[10^n]-Total[Boole[DigitCount[#,10,0]>0]&/@ Prime[ Range[ PrimePi[ 10^n]]]],{n,8}] (* The program generates the first 8 terms of the sequence. To generate more, increase the digit 8 but the program may take a long time to run. *) (* Harvey P. Dale, Aug 26 2021 *)

from sympy import sieve # use primerange for larger terms
def nodigs0(n): return '0' not in str(n)
def aupton(terms):
  ps, alst = 0, []
  for n in range(1, terms+1):
    ps += sum(nodigs0(p) for p in sieve.primerange(10**(n-1), 10**n))
    alst.append(ps)
  return alst
print(aupton(7)) # Michael S. Branicky, Apr 25 2021

Number of primes less than 10^n after removing any primes with at least one digit 0.
a(n) <= A052386(n) = 9*(9^n-1)/8. - Charles R Greathouse IV, Sep 13 2016
a(n) <= (9^n-1)/2 = A052386(n)*4/9 since the last digit of a prime of n digits can only be one of 4 numbers, (2,3,5,7) when n = 1 and (1,3,7,9) when n > 1. - Chai Wah Wu, Mar 18 2018

Edited and extended by Robert G. Wilson v, Feb 02 2004
a(9)-a(12) from Donovan Johnson, Feb 14 2008
a(13) from Robert Price, Nov 08 2013
a(14) from Giovanni Resta, Mar 20 2017

A024101 a(n) = 9^n-1.

Original entry on oeis.org

0, 8, 80, 728, 6560, 59048, 531440, 4782968, 43046720, 387420488, 3486784400, 31381059608, 282429536480, 2541865828328, 22876792454960, 205891132094648, 1853020188851840, 16677181699666568, 150094635296999120

Offset: 0

N. J. A. Sloane

Number of integers from 0 to 10^(n+1)-1 that lack any particular digit other than 0. - Robert G. Wilson v, Apr 14 2003

These are the numbers 888...8 in base 9. - Zerinvary Lajos, Nov 21 2007

Index entries for linear recurrences with constant coefficients, signature (10,-9).

Cf. A001019, A024023, A034472, A052386, A052379, A248726.

Table[9^n - 1, {n, 0, 20}]
LinearRecurrence[{10, -9}, {0, 8}, 30] (* Harvey P. Dale, Apr 14 2015 *)

a(n)=9^n-1 \\ Charles R Greathouse IV, Jun 11 2015

G.f.: 1/(1-9*x)-1/(1-x). - Mohammad K. Azarian, Jan 14 2009
E.g.f.: e^(9*x)-e^x. - Mohammad K. Azarian, Jan 14 2009
a(n) = A024023(n)*A034472(n). - Reinhard Zumkeller, Feb 14 2009
a(n) = 9*a(n-1)+8 for n>0, a(0)=0. - Vincenzo Librandi, Nov 19 2010
a(0)=0, a(1)=8; for n>1, a(n) = 10*a(n-1)-9*a(n-2). - Harvey P. Dale, Apr 14 2015
a(n) = Sum_{i=1..n} 8^i*binomial(n,n-i) for n>0, a(0)=0. - Bruno Berselli, Nov 11 2015
a(n) = A001019(n) - 1. - Sean A. Irvine, Jun 19 2019
Sum_{n>=1} 1/a(n) = A248726. - Amiram Eldar, Nov 13 2020

A228275 A(n,k) = Sum_{i=1..k} n^i; square array A(n,k), n>=0, k>=0, read by antidiagonals.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 6, 3, 0, 0, 4, 14, 12, 4, 0, 0, 5, 30, 39, 20, 5, 0, 0, 6, 62, 120, 84, 30, 6, 0, 0, 7, 126, 363, 340, 155, 42, 7, 0, 0, 8, 254, 1092, 1364, 780, 258, 56, 8, 0, 0, 9, 510, 3279, 5460, 3905, 1554, 399, 72, 9, 0

Offset: 0

Alois P. Heinz, Aug 19 2013

A(n,k) is the total sum of lengths of longest ending contiguous subsequences with the same value over all s in {1,...,n}^k:
A(4,1) = 4 = 1+1+1+1: [1], [2], [3], [4].
A(1,4) = 4: [1,1,1,1].
A(3,2) = 12 = 2+1+1+1+2+1+1+1+2: [1,1], [1,2], [1,3], [2,1], [2,2], [2,3], [3,1], [3,2], [3,3].
A(2,3) = 14 = 3+1+1+2+2+1+1+3: [1,1,1], [1,1,2], [1,2,1], [1,2,2], [2,1,1], [2,1,2], [2,2,1], [2,2,2].

			Square array A(n,k) begins:
  0, 0,  0,   0,    0,     0,      0,      0, ...
  0, 1,  2,   3,    4,     5,      6,      7, ...
  0, 2,  6,  14,   30,    62,    126,    254, ...
  0, 3, 12,  39,  120,   363,   1092,   3279, ...
  0, 4, 20,  84,  340,  1364,   5460,  21844, ...
  0, 5, 30, 155,  780,  3905,  19530,  97655, ...
  0, 6, 42, 258, 1554,  9330,  55986, 335922, ...
  0, 7, 56, 399, 2800, 19607, 137256, 960799, ...

Alois P. Heinz, Antidiagonals n = 0..140, flattened

Columns k=0-10 give: A000004, A001477, A002378, A027444, A027445, A152031, A228290, A228291, A228292, A228293, A228294.
Rows n=0-11 give: A000004, A001477, A000918(k+1), A029858(k+1), A080674, A104891, A105281, A104896, A052379(k-1), A052386, A105279, A105280.
Main diagonal gives A031972.
Lower diagonal gives A226238.
Cf. A228250.

A:= (n, k)-> `if`(n=1, k, (n/(n-1))*(n^k-1)):
seq(seq(A(n, d-n), n=0..d), d=0..12);

a[0, 0] = 0; a[1, k_] := k; a[n_, k_] := n*(n^k-1)/(n-1); Table[a[n-k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Dec 16 2013 *)

A(1,k) = k, else A(n,k) = n/(n-1)*(n^k-1).
A(n,k) = Sum_{i=1..k} n^i.
A(n,k) = Sum_{i=1..k+1} binomial(k+1,i)*A(n-i,k)*(-1)^(i+1) for n>k, given values A(0,k), A(1,k),..., A(k,k). - Yosu Yurramendi, Sep 03 2013

A082839 Decimal expansion of Kempner series Sum_{k >= 1, k has no digit 0 in base 10} 1/k.

Original entry on oeis.org

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

Offset: 2

Robert G. Wilson v, Apr 14 2003

"The most novel culling of the terms of the harmonic series has to be due to A. J. Kempner, who in 1914 considered what would happen if all terms are removed from it which have a particular digit appearing in their denominators. For example, if we choose the digits 7, we would exclude the terms with denominators such as 7, 27, 173, 33779, etc. There are 10 such series, each resulting from the removal of one of the digits 0, 1, 2, ..., 9 and the first question which naturally arises is just what percentage of the terms of the series are we removing by the process?"
"The sum of the reciprocals, 1 + 1/2 + 1/3 + 1/4 + 1/5 + ... [A002387] is unbounded. By taking sufficiently many terms, it can be made as large as one pleases. However, if the reciprocals of all numbers that when written in base 10 contain at least one 0 are omitted, then the sum has the limit, 23.10345... [Boas and Wrench, AMM v78]." - Wells.
Sums of this type are now called Kempner series, cf. LINKS. Convergence of the series is not more surprising than, and related to the fact that almost all numbers are pandigital (these have asymptotic density 1), i.e., "almost no number lacks any digit": Only a fraction of (9/10)^(L-1) of the L-digit numbers don't have a digit 0. Using L-1 = [log_10 k] ~ log_10 k, this density becomes 0.9^(L-1) ~ k^(log_10 0.9) ~ 1/k^0.046. If we multiply the generic term 1/k with this density, we have a converging series with value zeta(1 - log_10 0.9) ~ 22.4. More generally, almost all numbers contain any given substring of digits, e.g., 314159, and the sum over 1/k becomes convergent even if we omit just the terms having 314159 somewhere in their digits. - M. F. Hasler, Jan 13 2020

			23.10344790942054161603...

Paul Halmos, "Problems for Mathematicians, Young and Old", Dolciani Mathematical Expositions, 1991, p. 258.
Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, p. 34.
David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, England, 1997.

Robert Baillie, Sums of reciprocals of integers missing a given digit, Amer. Math. Monthly, 86 (1979), 372-374.
Robert Baillie, Summing The Curious Series Of Kempner And Irwin, arXiv:0806.4410 [math.CA], 2008-2015. [_Robert G. Wilson v_, Jun 01 2009]
Frank Irwin, A Curious Convergent Series, Amer. Math. Monthly, 23 (1916), 149-152.
A. D. Wadhwa, An interesting subseries of the harmonic series, Amer. Math. Monthly, 78 (1975), 931-933.
A. D. Wadhwa, Some convergent subseries of the harmonic series, Amer. Math. Monthly, 85 (1978), 661-663.
Eric Weisstein's World of Mathematics, Kempner Series.
Wikipedia, Kempner series
Wolfram Library Archive, KempnerSums.nb (8.6 KB) - Mathematica Notebook, Summing Kempner's Curious (Slowly-Convergent) Series [_Robert G. Wilson v_, Jun 01 2009]

Cf. A002387, A052386, A082830, A082831, A082832, A082833, A082834, A082835, A082836, A082837, A082838.

Cf. A052382 (zeroless numbers).

(* see the Mmca in Wolfram Library Archive. - Robert G. Wilson v, Jun 01 2009 *)

More terms from Robert G. Wilson v, Jun 01 2009

A052379 Number of integers from 1 to 10^(n+1)-1 that lack 0 and 1 as a digit.

Original entry on oeis.org

8, 72, 584, 4680, 37448, 299592, 2396744, 19173960, 153391688, 1227133512, 9817068104, 78536544840, 628292358728, 5026338869832, 40210710958664, 321685687669320, 2573485501354568, 20587884010836552, 164703072086692424, 1317624576693539400, 10540996613548315208

Offset: 0

Odimar Fabeny, Mar 12 2000

			For n=1, the numbers from 1 to 99 which have 0 or 1 as a digit are the numbers 1 and 10, 20, 30, ..., 90 and 11, 12, ..., 18, 19 and 21, 31, ..., 91. So a(1) = 99 - 27 = 72.

Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (9,-8).

Cf. A023001, A024101, A052386.

[(8^(n+2)-1)/7-1: n in [0..20]]; // Vincenzo Librandi, Jul 04 2011

A052379:=n->(8^(n+2)-1)/7-1: seq(A052379(n), n=0..20); # Wesley Ivan Hurt, Sep 26 2014

(8^(Range[0,20]+2)-1)/7-1 (* or *) LinearRecurrence[{9,-8},{8,72},20] (* Harvey P. Dale, Sep 22 2013 *)

a(n)=8^(n+2)\7 - 1 \\ Charles R Greathouse IV, Aug 25 2014

a(n) = (8^(n+2) - 1)/7 - 1.
G.f.: 8/((1-x)*(1-8*x)). - R. J. Mathar, Nov 19 2007
a(n) = 8*a(n-1) + 8.
a(n) = Sum_{k=1..n} 8^k. - corrected by Michel Marcus, Sep 25 2014
Conjecture: a(n) = A023001(n+2)-1. - R. J. Mathar, May 18 2007. Comment from Vim Wenders, Mar 26 2008: The conjecture is true: the g.f. leads to the closed form a(n) = -(8/7)*(1^n) + (64/7)*(8^n) = (-8 + 64*8^n)/7 = (-8 + 8^(n+2))/7 = (8^(n+2) - 1)/7 - 1 = A023001(n+2) - 1.
a(n) = 9*a(n-1) - 8*a(n-2); a(0)=8, a(1)=72. - Harvey P. Dale, Sep 22 2013
a(n) = 8*A023001(n+1). - Alois P. Heinz, Feb 15 2023

More terms and revised description from James Sellers, Mar 13 2000

A105279 a(0)=0; a(n) = 10*a(n-1) + 10.

Original entry on oeis.org

0, 10, 110, 1110, 11110, 111110, 1111110, 11111110, 111111110, 1111111110, 11111111110, 111111111110, 1111111111110, 11111111111110, 111111111111110, 1111111111111110, 11111111111111110, 111111111111111110, 1111111111111111110, 11111111111111111110, 111111111111111111110

Offset: 0

Alexandre Wajnberg, Apr 25 2005

a(n) is the smallest even number with digits in {0,1} having digit sum n; in other words, the base 10 reading of the binary string of A000918(n). Cf. A069532. - Jason Kimberley, Nov 02 2011

Also, except for a(0), the binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 645", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. - Robert Price, Jul 19 2017

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

Vincenzo Librandi, Table of n, a(n) for n = 0..100
Robert Price, Diagrams of first 20 stages of the Cellular Automata.
N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015.
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton.
S. Wolfram, A New Kind of Science.
Wolfram Research, Wolfram Atlas of Simple Programs.
Index entries for sequences related to cellular automata.
Index to 2D 5-Neighbor Cellular Automata.
Index to Elementary Cellular Automata.
Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A000918, A002275, A029858, A052379, A052386, A069532, A080674, A124166, A161770.
Row n=10 of A228275.
Partial sums of A178500.

a105279 n = a105279_list !! n
a105279_list = iterate ((* 10) . (+ 1)) 0
-- Reinhard Zumkeller, Feb 05 2012

[-10/9+(10/9)*10^n: n in [0..20]]; // Vincenzo Librandi, Jul 04 2011

NestList[10*(# + 1) &, 0, 25] (* Paolo Xausa, Jul 17 2024 *)

a(n) = (10/9)*(10^n - 1), with n>=0.
a(n) = Sum_{k=1..n} 10^k.
Repunits times 10: a(n) = 10 * A002275(n). - Reinhard Zumkeller, Feb 05 2012
From Stefano Spezia, Sep 15 2023: (Start)
O.g.f.: 10*x/((1 - x)*(1 - 10*x)).
E.g.f.: 10*exp(x)*(exp(9*x) - 1)/9. (End)
From Elmo R. Oliveira, Jun 18 2025: (Start)
a(n) = 11*a(n-1) - 10*a(n-2).
a(n) = A124166(n)/10.
a(n) = A161770(n)/100 for n >= 1. (End)

A104891 a(0) = 0; a(n) = 5*a(n-1) + 5.

Original entry on oeis.org

0, 5, 30, 155, 780, 3905, 19530, 97655, 488280, 2441405, 12207030, 61035155, 305175780, 1525878905, 7629394530, 38146972655, 190734863280, 953674316405, 4768371582030, 23841857910155, 119209289550780, 596046447753905, 2980232238769530, 14901161193847655

Offset: 0

Alexandre Wajnberg, Apr 24 2005

Number of integers from 0 to (10^n)-1 that lack 0, 1, 2, 3 and 4 as a digit.

Number of monic irreducible polynomials of degree 1 in GF(5)[x1,...,xn]. - Max Alekseyev, Jan 23 2006

			a(3) = 5*a(2) + 5 = 5*30 + 5 = 155.

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-5).

Cf. A000225, A000918, A029858, A052379, A052386, A080674.

Row n=5 of A228275.

[5*(5^n -1)/4: n in [0..30]]; // G. C. Greubel, Jun 15 2021

a:=n->add(5^j,j=1..n): seq(a(n),n=0..30); # Zerinvary Lajos, Jun 27 2007

RecurrenceTable[{a[n]==5*a[n-1]+5, a[0]==0}, a, {n, 0, 30}] (* Vaclav Kotesovec, Jul 25 2014 *)
NestList[5#+5&,0,30] (* Harvey P. Dale, Oct 04 2019 *)

concat(0, Vec(5*x/((x-1)*(5*x-1)) + O(x^30))) \\ Colin Barker, Jul 25 2014

[5*(5^n -1)/4 for n in (0..30)] # G. C. Greubel, Jun 15 2021

a(n) = 5*(5^n - 1)/4. - Max Alekseyev, Jan 23 2006
a(n) = a(n-1) + 5^n with a(0)=0. - Vincenzo Librandi, Nov 13 2010
From Colin Barker, Jul 25 2014: (Start)
a(n) = 6*a(n-1) - 5*a(n-2).
G.f.: 5*x / ((1-x)*(1-5*x)). (End)
E.g.f.: (5/4)*(exp(5*x) - exp(x)). - G. C. Greubel, Jun 15 2021

A104896 a(0) = 0; a(n) = 7*a(n-1) + 7.

Original entry on oeis.org

0, 7, 56, 399, 2800, 19607, 137256, 960799, 6725600, 47079207, 329554456, 2306881199, 16148168400, 113037178807, 791260251656, 5538821761599, 38771752331200, 271402266318407, 1899815864228856, 13298711049601999, 93090977347214000, 651636841430498007

Offset: 0

Alexandre Wajnberg, Apr 24 2005

Conjecture: this is also the number of integers from 0 to 10^n - 1 that lack 0, 1 and 2 as a digit.

Number of monic irreducible polynomials of degree 1 in GF(7)[x1,...,xn]. - Max Alekseyev, Jan 23 2006

Alois P. Heinz, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (8,-7).

Cf. A000918, A029858, A052379, A052386, A080674.

Row n=7 of A228275.

[(7/6)*(7^n -1): n in [0..30]]; // G. C. Greubel, Jun 09 2021

a:=n->sum (7^j,j=1..n): seq(a(n), n=0..30); # Zerinvary Lajos, Oct 03 2007

RecurrenceTable[{a[n]==7*a[n-1]+7,a[0]==0},a,{n,0,30}] (* Vaclav Kotesovec, Jul 25 2014 *)

concat(0, Vec(7*x/((x-1)*(7*x-1)) + O(x^30))) \\ Colin Barker, Jul 25 2014

[(7/6)*(7^n -1) for n in (0..30)] # G. C. Greubel, Jun 09 2021

a(n) = (7^(n+1) - 7) / 6. - Max Alekseyev, Jan 23 2006
a(n) = a(n-1) + 7^n with a(0)=0. - Vincenzo Librandi, Nov 13 2010
From Colin Barker, Jul 25 2014: (Start)
a(n) = 8*a(n-1) - 7*a(n-2).
G.f.: 7*x / ((x-1)*(7*x-1)). (End)
E.g.f.: (7/6)*(exp(7*x) - exp(x)). - G. C. Greubel, Jun 09 2021

A105281 a(0)=0; a(n) = 6*a(n-1) + 6.

Original entry on oeis.org

0, 6, 42, 258, 1554, 9330, 55986, 335922, 2015538, 12093234, 72559410, 435356466, 2612138802, 15672832818, 94036996914, 564221981490, 3385331888946, 20311991333682, 121871948002098, 731231688012594, 4387390128075570, 26324340768453426, 157946044610720562

Offset: 0

Alexandre Wajnberg, Apr 25 2005

Number of integers from 0 to (10^n) - 1 that lack 0, 1, 2 and 3 as a digit.

a(n) is the expected number of tosses of a single die needed to obtain for the first time a string of n consecutive 6's. - Jean M. Morales, Aug 04 2012

Index entries for linear recurrences with constant coefficients, signature (7,-6).

Cf. A000918, A003464, A029858, A052379, A052386, A080674.

Row n=6 of A228275.

a:=n->add(6^j,j=1..n): seq(a(n),n=0..30); # Zerinvary Lajos, Oct 03 2007

NestList[6#+6&,0,30] (* Harvey P. Dale, Jul 24 2012 *)

PARI
```
a(n)=if(n<0,0, (6^n-1)*6/5)
```

a(n) = 6^n + a(n-1) (with a(0)=0). - Vincenzo Librandi, Nov 13 2010
From Colin Barker, Jan 28 2013: (Start)
a(n) = 7*a(n-1) - 6*a(n-2).
G.f.: 6*x/((x-1)*(6*x-1)). (End)
From Elmo R. Oliveira, Mar 16 2025: (Start)
E.g.f.: 6*exp(x)*(exp(5*x) - 1)/5.
a(n) = 6*(6^n - 1)/5.
a(n) = 6*A003464(n). (End)

More terms from Harvey P. Dale, Jul 24 2012

A105280 a(0)=0; a(n) = 11*a(n-1) + 11.

Original entry on oeis.org

0, 11, 132, 1463, 16104, 177155, 1948716, 21435887, 235794768, 2593742459, 28531167060, 313842837671, 3452271214392, 37974983358323, 417724816941564, 4594972986357215, 50544702849929376, 555991731349223147, 6115909044841454628, 67274999493256000919, 740024994425816010120

Offset: 0

Alexandre Wajnberg, Apr 25 2005

Harvey P. Dale, Table of n, a(n) for n = 0..960
Index entries for linear recurrences with constant coefficients, signature (12,-11).

Cf. A000918, A016123, A029858, A052379, A052386, A080674.

Row n=11 of A228275.

a:=n-> add(11^j,j=1..n): seq(a(n),n=0..12); # Zerinvary Lajos, Oct 03 2007

NestList[11#+11&,0,20] (* or *) LinearRecurrence[{12,-11},{0,11},20] (* Harvey P. Dale, Dec 02 2023 *)

a(n) = 11^n + a(n-1) (with a(0)=0). - Vincenzo Librandi, Nov 13 2010
From Elmo R. Oliveira, May 24 2025: (Start)
G.f.: 11*x/((x-1)*(11*x-1)).
E.g.f.: 11*exp(x)*(exp(10*x) - 1)/10.
a(n) = 11*(11^n - 1)/10.
a(n) = 12*a(n-1) - 11*a(n-2).
a(n) = A016123(n) - 1. (End)

Corrected by T. D. Noe, Nov 07 2006

cp's OEIS Frontend

A091634 Number of primes less than 10^n which do not contain the digit 0.

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A024101 a(n) = 9^n-1.

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A228275 A(n,k) = Sum_{i=1..k} n^i; square array A(n,k), n>=0, k>=0, read by antidiagonals.

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A082839 Decimal expansion of Kempner series Sum_{k >= 1, k has no digit 0 in base 10} 1/k.

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A052379 Number of integers from 1 to 10^(n+1)-1 that lack 0 and 1 as a digit.

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A105279 a(0)=0; a(n) = 10*a(n-1) + 10.

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Haskell

Magma

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A104891 a(0) = 0; a(n) = 5*a(n-1) + 5.

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