A086578 -id:A086578 - cp's OEIS frontend

A086574 a(n) = 3*(10^n - 1).

0, 27, 297, 2997, 29997, 299997, 2999997, 29999997, 299999997, 2999999997, 29999999997, 299999999997, 2999999999997, 29999999999997, 299999999999997, 2999999999999997, 29999999999999997, 299999999999999997, 2999999999999999997, 29999999999999999997, 299999999999999999997

Offset: 0

Ray Chandler, Jul 22 2003

Original definition: a(n) = k where R(k+3) = 3. [Here R = reverse = A004086, not R = repunit = A002275 as in some other places.]

The restriction to positive indices yields A083813. - M. F. Hasler, Jul 29 2016

Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A002275, A004086 (R(n)), A083813.

Cf. One of family of sequences of form a(n) = k, where R(k+m) = m, m=1 to 9; m=1: A002283, m=2: A086573, m=3: A086574, m=4: A086575, m=5: A086576, m=6: A086577, m=7: A086578, m=8: A086579, m=9: A086580.

Join[{0},Table[FromDigits[Join[PadRight[{2},n,9],{7}]],{n,20}]] (* or *) LinearRecurrence[{11,-10},{0,27},30] (* Harvey P. Dale, Nov 28 2015 *)

a(n)=10^n*3-3 \\ M. F. Hasler, Jul 29 2016

a(n) = 3*9*A002275(n) = 3*A002283(n).
R(a(n)) = A086579(n).
a(n) = 11*a(n-1) - 10*a(n-2) with a(0)=0 and a(1)=27. - Harvey P. Dale, Nov 28 2015
G.f.: 27*x/((1 - x)*(1 - 10*x)). - Ilya Gutkovskiy, Jul 29 2016
E.g.f.: 3*exp(x)*(exp(9*x) - 1). - Elmo R. Oliveira, Sep 12 2024

Edited by M. F. Hasler, Jul 29 2016

A086573 a(n) = 2*(10^n - 1).

Original entry on oeis.org

0, 18, 198, 1998, 19998, 199998, 1999998, 19999998, 199999998, 1999999998, 19999999998, 199999999998, 1999999999998, 19999999999998, 199999999999998, 1999999999999998, 19999999999999998, 199999999999999998, 1999999999999999998, 19999999999999999998, 199999999999999999998

Offset: 0

Ray Chandler, Jul 22 2003

Original definition: a(n) = k where R(k+2) = 2.

Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A002275, A004086 (R(n)), A083812.

One of family of sequences of form a(n) = k, where R(k+m) = m, m=1 to 9; m=1: A002283, m=2: A086573, m=3: A086574, m=4: A086575, m=5: A086576, m=6: A086577, m=7: A086578, m=8: A086579, m=9: A086580.

a(n) = 2*9*A002275(n) = 2*A002283(n).
R(a(n)) = A086580(n).
From Chai Wah Wu, Jul 08 2016: (Start)
a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.
G.f.: 18*x/((1 - x)*(1 - 10*x)). (End)
E.g.f.: 2*exp(x)*(exp(9*x) - 1). - Elmo R. Oliveira, Sep 12 2024

Edited by Jinyuan Wang, Aug 04 2021

A086580 a(n) = 9*(10^n - 1).

Original entry on oeis.org

0, 81, 891, 8991, 89991, 899991, 8999991, 89999991, 899999991, 8999999991, 89999999991, 899999999991, 8999999999991, 89999999999991, 899999999999991, 8999999999999991, 89999999999999991, 899999999999999991, 8999999999999999991, 89999999999999999991, 899999999999999999991

Offset: 0

Ray Chandler, Jul 22 2003

Original definition: a(n) = k where R(k+9) = 9.

G. C. Greubel, Table of n, a(n) for n = 0..990
Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A002275, A004086 (R(n)), A086573.

One of family of sequences of form a(n) = k, where R(k+m) = m, m=1 to 9; m=1: A002283, m=2: A086573, m=3: A086574, m=4: A086575, m=5: A086576, m=6: A086577, m=7: A086578, m=8: A086579, m=9: A086580.

[9*(10^n -1): n in [0..30]]; // G. C. Greubel, Jul 07 2023

Table[9*(10^n-1), {n,0,30}] (* G. C. Greubel, Jul 07 2023 *)

A086580=BinaryRecurrenceSequence(11,-10,0,81)
[A086580(n) for n in range(30)] # G. C. Greubel, Jul 07 2023

a(n) = 9*9*A002275(n) = 9*A002283(n).
R(a(n)) = A086573(n).
From Chai Wah Wu, Jul 08 2016: (Start)
a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.
G.f.: 81*x/((1 - x)*(1 - 10*x)). (End)
E.g.f.: 9*exp(x)*(exp(9*x) - 1). - Elmo R. Oliveira, Sep 12 2024

Name edited by Jinyuan Wang, Aug 04 2021

A086575 a(n) = 4*(10^n - 1).

Original entry on oeis.org

0, 36, 396, 3996, 39996, 399996, 3999996, 39999996, 399999996, 3999999996, 39999999996, 399999999996, 3999999999996, 39999999999996, 399999999999996, 3999999999999996, 39999999999999996, 399999999999999996, 3999999999999999996, 39999999999999999996, 399999999999999999996

Offset: 0

Ray Chandler, Jul 22 2003

Original definition: a(n) = k where R(k+4) = 4.

Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A002275, A004086 (R(n)), A083811.

One of family of sequences of form a(n) = k, where R(k+m) = m, m=1 to 9; m=1: A002283, m=2: A086573, m=3: A086574, m=4: A086575, m=5: A086576, m=6: A086577, m=7: A086578, m=8: A086579, m=9: A086580.

LinearRecurrence[{11,-10},{0,36},20] (* Harvey P. Dale, May 14 2017 *)

a(n) = 4*9*A002275(n) = 4*A002283(n).
R(a(n)) = A086578(n).
From Chai Wah Wu, Jul 08 2016: (Start)
a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.
G.f.: 36*x/((1 - x)*(1 - 10*x)). (End)
E.g.f.: 4*exp(x)*(exp(9*x) - 1). - Elmo R. Oliveira, Sep 12 2024

Edited by Jinyuan Wang, Aug 04 2021

A086576 a(n) = 5*(10^n - 1).

Original entry on oeis.org

0, 45, 495, 4995, 49995, 499995, 4999995, 49999995, 499999995, 4999999995, 49999999995, 499999999995, 4999999999995, 49999999999995, 499999999999995, 4999999999999995, 49999999999999995, 499999999999999995, 4999999999999999995, 49999999999999999995, 499999999999999999995

Offset: 0

Ray Chandler, Jul 22 2003

Original definition: a(n) = k where R(k+5) = 5.

			From _John Elias_, Jun 23 2021: (Start)
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45;
11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99 = 495;
111 + 222 + 333 + 444 + 555 + 666 + 777 + 888 + 999 = 4995;
1111 + 2222 + 3333 + 4444 + 5555 + 6666 + 7777 + 8888 + 9999 = 49995;
11111 + 22222 + 33333 + 44444 + 55555 + 66666 + 77777 + 88888 + 99999 = 499995; etc. (End)

Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A002275, A004086 (R(n)).

Cf. One of family of sequences of form a(n)=k, where R(k+m)=m, m = 1 to 9; m=1: A002283, m=2: A086573, m=3: A086574, m=4: A086575, m=5: A086576, m=6: A086577, m=7: A086578, m=8: A086579, m=9: A086580.

Join[{0}, LinearRecurrence[{11,-10},{45,495},50]] (* G. C. Greubel, Jul 08 2016 *)

a(n) = 5*9*A002275(n) = 5*A002283(n).
R(a(n)) = A086577(n).
From Chai Wah Wu, Jul 08 2016: (Start)
a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.
G.f.: 45*x/((1 - x)*(1 - 10*x)). (End)
E.g.f.: 5*exp(x)*(exp(9*x) - 1). - Elmo R. Oliveira, Sep 12 2024

Name edited by Jinyuan Wang, Aug 04 2021

A086577 a(n) = 6*(10^n - 1).

Original entry on oeis.org

0, 54, 594, 5994, 59994, 599994, 5999994, 59999994, 599999994, 5999999994, 59999999994, 599999999994, 5999999999994, 59999999999994, 599999999999994, 5999999999999994, 59999999999999994, 599999999999999994, 5999999999999999994, 59999999999999999994, 599999999999999999994

Offset: 0

Ray Chandler, Jul 22 2003

Original definition: a(n) = k where R(k+6) = 6.

Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A002275, A004086 (R(n)).

One of a family of sequences of the form "Numbers k such that reverse(k+m) = m", m = 1 to 9; m=1: A002283, m=2: A086573, m=3: A086574, m=4: A086575, m=5: A086576, m=6: A086577, m=7: A086578, m=8: A086579, m=9: A086580.

LinearRecurrence[{11,-10},{0,54},30] (* Harvey P. Dale, Nov 27 2022 *)

a(n) = 6*9*A002275(n) = 6*A002283(n).
R(a(n)) = A086576(n).
From Chai Wah Wu, Jul 08 2016: (Start)
a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.
G.f.: 54*x/((1 - x)*(1 - 10*x)). (End)
E.g.f.: 6*exp(x)*(exp(9*x) - 1). - Elmo R. Oliveira, Sep 12 2024

Name edited by Jinyuan Wang, Aug 04 2021

A086579 a(n) = 8*(10^n - 1).

Original entry on oeis.org

0, 72, 792, 7992, 79992, 799992, 7999992, 79999992, 799999992, 7999999992, 79999999992, 799999999992, 7999999999992, 79999999999992, 799999999999992, 7999999999999992, 79999999999999992, 799999999999999992, 7999999999999999992, 79999999999999999992, 799999999999999999992

Offset: 0

Ray Chandler, Jul 22 2003

Original definition: a(n) = k where R(k+8) = 8.

Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A002275, A004086 (R(n)).

One of family of sequences of form a(n) = k, where R(k+m) = m, m=1 to 9; m=1: A002283, m=2: A086573, m=3: A086574, m=4: A086575, m=5: A086576, m=6: A086577, m=7: A086578, m=8: A086579, m=9: A086580.

LinearRecurrence[{11,-10},{0,72},30] (* Harvey P. Dale, Mar 22 2025 *)

a(n) = 8*9*A002275(n) = 8*A002283(n).
R(a(n)) = A086574(n).
From Chai Wah Wu, Jul 08 2016: (Start)
a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.
G.f.: 72*x/((1 - x)*(1 - 10*x)). (End)
E.g.f.: 8*exp(x)*(exp(9*x) - 1). - Elmo R. Oliveira, Sep 12 2024

Edited by Jinyuan Wang, Aug 04 2021

A100412 a(n) = 8*10^n - 7.

Original entry on oeis.org

1, 73, 793, 7993, 79993, 799993, 7999993, 79999993, 799999993, 7999999993, 79999999993, 799999999993, 7999999999993, 79999999999993, 799999999999993, 7999999999999993, 79999999999999993, 799999999999999993

Offset: 0

Farideh Firoozbakht, Dec 08 2004

Also: Numbers n such that n is reversal(n)-th odd number. (This was the original definition. - Ed.)

All semiprimes in this sequence (n = 2, 4, 7, 9, 11, 16, 18, 23, 31, 32, 40, ...) are in A136543. - M. F. Hasler, Nov 03 2012

			793 is in the sequence because 793 is 397th odd number.
1 is in the sequence because 1 is the 1st odd number. - _M. F. Hasler_, Nov 03 2012

G. C. Greubel, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A100413, A136543.

Sequences of the form m*10^n - 7: 3*A033175 (m=1, 10), A086943 (m=3), 3*A185127 (m=4), A086578 (m=7), this sequence (m=8).

[8*10^n -7: n in [0..20]]; // G. C. Greubel, Apr 14 2023

Mathematica
```
Table[8*10^n-7, {n,0,20}]
```

A100412(n):=8*10^n-7$
makelist(A100412(n),n,0,17); /* Martin Ettl, Nov 08 2012 */

Vec((1+62*x)/((1-x)*(1-10*x)) + O(x^100)) \\ Colin Barker, Oct 14 2014

[8*10^n -7 for n in range(21)] # G. C. Greubel, Apr 14 2023

From Colin Barker, Oct 14 2014: (Start)
a(n) = 10*a(n-1) + a(n-2) - 10*a(n-3).
G.f.: (1+62*x)/((1-x)*(1-10*x)). (End)
E.g.f.: 8*exp(10*x) - 7*exp(x). - G. C. Greubel, Apr 14 2023

Edited and extended to offset 0 by M. F. Hasler, Nov 03 2012

cp's OEIS Frontend

A086574 a(n) = 3*(10^n - 1).

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A086573 a(n) = 2*(10^n - 1).

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A086580 a(n) = 9*(10^n - 1).

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A086575 a(n) = 4*(10^n - 1).

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A086576 a(n) = 5*(10^n - 1).

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A086577 a(n) = 6*(10^n - 1).

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A086579 a(n) = 8*(10^n - 1).

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