A087052 -id:A087052 - cp's OEIS frontend

A051885 Smallest number whose sum of digits is n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 29, 39, 49, 59, 69, 79, 89, 99, 199, 299, 399, 499, 599, 699, 799, 899, 999, 1999, 2999, 3999, 4999, 5999, 6999, 7999, 8999, 9999, 19999, 29999, 39999, 49999, 59999, 69999, 79999, 89999, 99999, 199999, 299999, 399999, 499999

Offset: 0

Felice Russo, Dec 15 1999

This is also the list of lunar triangular numbers: A087052 with duplicates removed. - N. J. A. Sloane, Jan 25 2011
Numbers n such that A061486(n) = n. - Amarnath Murthy, May 06 2001
The product of digits incremented by 1 is the same as the number incremented by 1. If a(n) = abcd...(a,b,c,d, etc. are digits of a(n)) {a(n) + 1} = (a+1)*(b+1)(c+1)*(d+1)*..., e.g., 299 + 1 = (2+1)*(9+1)*(9+1) = 300. - Amarnath Murthy, Jul 29 2003
A138471(a(n)) = 0. - Reinhard Zumkeller, Mar 19 2008
a(n+1) = A108971(A179988(n)). - Reinhard Zumkeller, Aug 09 2010, Jul 10 2011
Positions of records in A003132: A080151(n) = A003132(a(n)). - Reinhard Zumkeller, Jul 10 2011
a(n) = A242614(n,1). - Reinhard Zumkeller, Jul 16 2014
A254524(a(n)) = 1. - Reinhard Zumkeller, Oct 09 2015
The slowest strictly increasing sequence of nonnegative integers such that, for any two terms, calculating the difference of their decimal representations requires no borrowing. - Rick L. Shepherd, Aug 11 2017

Iain Fox, Table of n, a(n) for n = 0..9000 (first 101 terms from Reinhard Zumkeller)
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, arXiv:1107.1130 [math.NT], 2011. [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
A. Murthy, Exploring some new ideas on Smarandache type sets, functions and sequences, Smarandache Notions Journal Vol. 11 N. 1-2-3 Spring 2000.
Index entries for sequences related to dismal (or lunar) arithmetic
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,10,-10).

Cf. A061104, A061105, A061486, A007953, A067043, A087052.
Numbers of form i*b^j-1 (i=1..b-1, j >= 0) for bases b = 2 through 9: A000225, A062318, A180516, A181287, A181288, A181303, A165804, A140576. - N. J. A. Sloane, Jan 25 2011
Cf. A002283.
Cf. A254524.

a051885 n = (m + 1) * 10^n' - 1 where (n',m) = divMod n 9
-- Reinhard Zumkeller, Jul 10 2011

Magma
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[i*10^j-1: i in [1..9], j in [0..5]];
```

b:=10; t1:=[]; for j from 0 to 15 do for i from 1 to b-1 do t1:=[op(t1), i*b^j-1]; od: od: t1; # N. J. A. Sloane, Jan 25 2011

a[n_] := (Mod[n, 9] + 1)*10^Floor[n/9] - 1; Table[a[n], {n, 0, 49}](* Jean-François Alcover, Dec 01 2011, after Henry Bottomley *)

A051885(n) = (n%9+1)*10^(n\9)-1  \\ M. F. Hasler, Jun 17 2012

first(n) = Vec(x*(x^2 + x + 1)*(x^6 + x^3 + 1)/((x - 1)*(10*x^9 - 1)) + O(x^n), -n) \\ Iain Fox, Dec 30 2017

def A051885(n): return ((n % 9)+1)*10**(n//9)-1 # Chai Wah Wu, Apr 04 2021

These are the numbers i*10^j-1 (i=1..9, j >= 0). - N. J. A. Sloane, Jan 25 2011
a(n) = ((n mod 9) + 1)*10^floor(n/9) - 1 = a(n-1) + 10^floor((n-1)/9). - Henry Bottomley, Apr 24 2001
a(n) = A037124(n+1) - 1. - Reinhard Zumkeller, Jan 03 2008, Jul 10 2011
G.f.: x*(x^2+x+1)*(x^6+x^3+1) / ((x-1)*(10*x^9-1)). - Colin Barker, Feb 01 2013

More terms from James Sellers, Dec 16 1999

Offset fixed by Reinhard Zumkeller, Jul 10 2011

A343045 a(0) = 0 and for any n > 0, a(n) = A343044(a(n-1), n).

Original entry on oeis.org

0, 1, 3, 3, 5, 5, 11, 11, 11, 11, 11, 11, 17, 17, 17, 17, 17, 17, 23, 23, 23, 23, 23, 23, 29, 29, 29, 29, 29, 29, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 89, 89, 89, 89, 89, 89, 89

Offset: 0

Rémy Sigrist, Apr 05 2021

This sequence has similarities with A087052 and A343041.

If we remove duplicate terms, then we obtain A343048.

			The first terms, in decimal and in primorial base, are:
  n   a(n)  prim(n)  prim(a(n))
  --  ----  -------  ----------
   0     0        0           0
   1     1        1           1
   2     3       10          11
   3     3       11          11
   4     5       20          21
   5     5       21          21
   6    11      100         121
   7    11      101         121
   8    11      110         121
   9    11      111         121
  10    11      120         121
  11    11      121         121
  12    17      200         221
  13    17      201         221
  14    17      210         221

Rémy Sigrist, Table of n, a(n) for n = 0..10000
Rémy Sigrist, PARI program for A343045
Index entries for sequences related to dismal (or lunar) arithmetic
Index entries for sequences related to primorial base

Cf. A343041, A343044, A343048.

Cf. A087052.

PARI
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See Links section.
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A087121 Take bounded lunar divisors of n as defined in A087028, add them using lunar addition. See A087082 for their conventional sum.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 199, 109, 109, 109, 109, 109, 109, 109, 109, 109, 199, 199

Offset: 1

Marc LeBrun and N. J. A. Sloane, Oct 21 2003

Differs from A087052 after 100 terms.

D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
Index entries for sequences related to dismal (or lunar) arithmetic

Cf. A087061, A087062, A087028, A087083, A087082.

A342766 a(1) = 1, for any n > 1, a(n) = A342765(a(n-1), n).

Original entry on oeis.org

1, 2, 3, 6, 10, 10, 14, 28, 42, 42, 66, 66, 78, 78, 78, 156, 204, 204, 228, 228, 228, 228, 276, 276, 460, 460, 690, 690, 870, 870, 930, 1860, 1860, 1860, 1860, 1860, 2220, 2220, 2220, 2220, 2460, 2460, 2580, 2580, 2580, 2580, 2820, 2820, 3948, 3948, 3948, 3948

Offset: 1

Rémy Sigrist, Apr 02 2021

nonn

This sequence has similarities with A087052.
This sequence is nondecreasing.
A new value is introduced at each power of prime (A000961).
The ordinal transform of the sequence is A276781.
The RUNS transform of the sequence is A057820.

			The first terms, alongside their prime factorizations, are:
  n   a(n)  n          a(n)
  --  ----  ---------  ----------
   1     1          1           1
   2     2          2           2
   3     3          3           3
   4     6      2 * 2       2 * 3
   5    10          5       2 * 5
   6    10      2 * 3       2 * 5
   7    14          7       2 * 7
   8    28  2 * 2 * 2   2 * 2 * 7
   9    42      3 * 3   2 * 3 * 7
  10    42      2 * 5   2 * 3 * 7
  11    66         11   2 * 3 * 11
  12    66  2 * 2 * 3   2 * 3 * 11

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A342766
Index entries for sequences related to dismal (or lunar) arithmetic

Cf. A000961, A057820, A087052, A276781, A342765.

PARI
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See Links section.
```

A343041 a(0) = 0 and for any n > 0, a(n) = A343040(a(n-1), n).

Original entry on oeis.org

0, 1, 3, 3, 5, 5, 11, 11, 11, 11, 11, 11, 17, 17, 17, 17, 17, 17, 23, 23, 23, 23, 23, 23, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71

Offset: 0

Rémy Sigrist, Apr 03 2021

This sequence has similarities with A087052.
If we remove duplicate terms, then we obtain A200748.
The value A200748(k) appears A130493(k) times for any k > 0.

			The first terms, in decimal and in factorial base, are:
  n   a(n)  fact(n)  fact(a(n))
  --  ----  -------  ----------
   0     0        0           0
   1     1        1           1
   2     3       10          11
   3     3       11          11
   4     5       20          21
   5     5       21          21
   6    11      100         121
   7    11      101         121
   8    11      110         121
   9    11      111         121
  10    11      120         121
  11    11      121         121
  12    17      200         221
  13    17      201         221
  14    17      210         221

Rémy Sigrist, Table of n, a(n) for n = 0..5039
Rémy Sigrist, PARI program for A343041
Index entries for sequences related to dismal (or lunar) arithmetic
Index entries for sequences related to factorial base representation

Cf. A087052, A130493, A200748, A343040, A343045.

PARI
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See Links section.
```

cp's OEIS Frontend

A051885 Smallest number whose sum of digits is n.

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A343045 a(0) = 0 and for any n > 0, a(n) = A343044(a(n-1), n).

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A087121 Take bounded lunar divisors of n as defined in A087028, add them using lunar addition. See A087082 for their conventional sum.

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A342766 a(1) = 1, for any n > 1, a(n) = A342765(a(n-1), n).

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PARI

A343041 a(0) = 0 and for any n > 0, a(n) = A343040(a(n-1), n).

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