A086943 -id:A086943 - cp's OEIS frontend

A086578 a(n) = 7*(10^n - 1).

0, 63, 693, 6993, 69993, 699993, 6999993, 69999993, 699999993, 6999999993, 69999999993, 699999999993, 6999999999993, 69999999999993, 699999999999993, 6999999999999993, 69999999999999993, 699999999999999993, 6999999999999999993, 69999999999999999993, 699999999999999999993

Offset: 0

Ray Chandler, Jul 22 2003

Original definition: a(n) = k where R(k+7) = 7.

G. C. Greubel, Table of n, a(n) for n = 0..500
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.
Sequences of the form m*10^n - 7: 3*A033175 (m=1, 10), A086943 (m=3), 3*A185127 (m=4), this sequence (m=7), A100412 (m=8).

[7*(10^n -1): n in [0..20]]; // G. C. Greubel, Apr 14 2023

LinearRecurrence[{11,-10}, {0,63}, 31] (* G. C. Greubel, Apr 14 2023 *)

[7*(10^n -1) for n in range(21)] # G. C. Greubel, Apr 14 2023

a(n) = 7*9*A002275(n) = 7*A002283(n).
R(a(n)) = A086575(n).
From Chai Wah Wu, Jul 08 2016: (Start)
a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.
G.f.: 63*x/((1 - x)*(1 - 10*x)). (End)
E.g.f.: 7*(exp(10*x) - exp(x)). - G. C. Greubel, Apr 14 2023

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

A086942 Integers k such that R(k+8) = 4.

Original entry on oeis.org

32, 392, 3992, 39992, 399992, 3999992, 39999992, 399999992, 3999999992, 39999999992, 399999999992, 3999999999992, 39999999999992, 399999999999992, 3999999999999992, 39999999999999992, 399999999999999992, 3999999999999999992, 39999999999999999992

Offset: 1

Ray Chandler, Jul 24 2003

Vincenzo Librandi, Table of n, a(n) for n = 1..300
Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A004086, A086940, A086943, A099150, A198971.

[4*10^n-8: n in [1..25]]; // Vincenzo Librandi, Aug 22 2011

4*10^Range[20] - 8 (* Paolo Xausa, Sep 21 2024 *)

a(n) = 4*10^n - 8.
R(a(n)) = A086943(n).
G.f.: 8*x*(5*x+4)/((10*x-1)*(x-1)).
a(n) = 8*A198971(n-1).
From Elmo R. Oliveira, May 01 2025: (Start)
E.g.f.: 4*(1 - 2*exp(x) + exp(10*x)).
a(n) = 4*A099150(n) = 2*A086940(n).
a(n) = 11*a(n-1) - 10*a(n-2) for n > 2. (End)

A100413 Numbers k such that k is reversal(k)-th even composite number (k is A004086(k)-th even composite number).

Original entry on oeis.org

52, 592, 5992, 59992, 599992, 5999992, 59999992, 599999992, 5999999992, 59999999992, 599999999992, 5999999999992, 59999999999992, 599999999999992, 5999999999999992, 59999999999999992, 599999999999999992

Offset: 1

Farideh Firoozbakht, Dec 08 2004

			592 is in the sequence because 592 is the 295th even composite number.

G. C. Greubel, Table of n, a(n) for n = 1..500
Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A004086, A086943, A100412.

[6*10^n -8: n in [1..20]]; // G. C. Greubel, Apr 13 2023

A100413:=n->6*10^n-8; seq(A100413(n), n=1..20); # Wesley Ivan Hurt, Apr 06 2014

Mathematica
```
Table[6*10^n-8, {n,20}]
```

A100413(n):=6*10^n-8$
makelist(A100413(n),n,1,17); /* Martin Ettl, Nov 08 2012 */

Vec(4*x*(5*x+13)/((x-1)*(10*x-1)) + O(x^100)) \\ Colin Barker, Oct 14 2014

[6*10^n -8 for n in range(1,21)] # G. C. Greubel, Apr 13 2023

a(n) = 6*10^n - 8.
a(n) = 2*(A086943(n) + 3). - Martin Ettl, Nov 08 2012
From Colin Barker, Oct 14 2014: (Start)
a(n) = 10*a(n-1) + a(n-2) - 10*a(n-3).
G.f.: 4*x*(13+5*x)/((1-x)*(1-10*x)). (End)
E.g.f.: 2 (1 - 4*exp(x) + 3*exp(10*x)). - G. C. Greubel, Apr 13 2023

cp's OEIS Frontend

A086578 a(n) = 7*(10^n - 1).

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

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A086942 Integers k such that R(k+8) = 4.

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A100413 Numbers k such that k is reversal(k)-th even composite number (k is A004086(k)-th even composite number).

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