A188165 -id:A188165 - cp's OEIS frontend

A240942 Numbers k that divide 2^k + 9.

1, 11, 121, 323, 117283, 432091, 4132384531, 15516834659, 15941429747, 98953554491, 3272831195051, 7362974489179, 26306805687881, 33869035218491, 280980898827691

Offset: 1

Derek Orr, Aug 04 2014

No other terms below 10^15. Some larger terms: 53496121130110340001650284048539458491, 136243118444105327963550175410279542214992801356720577. - Max Alekseyev, Sep 29 2016

			2^11 + 9 = 2057 is divisible by 11. Thus 11 is a term of this sequence.

OEIS Wiki, 2^n mod n

Cf. A051447, A188165, A245594, A245319, A245318, A244673.

select(n -> 9 + 2 &^ n mod n = 0, [$1..10^6]); # Robert Israel, Aug 04 2014

for(n=1,10^9, if(Mod(2,n)^n==-9, print1(n,", "); ); );

a(7)-a(10) from Lars Blomberg, Nov 05 2014

a(11)-a(15) from Max Alekseyev, Sep 29 2016

A242475 a(n) = 2^n + 8.

Original entry on oeis.org

9, 10, 12, 16, 24, 40, 72, 136, 264, 520, 1032, 2056, 4104, 8200, 16392, 32776, 65544, 131080, 262152, 524296, 1048584, 2097160, 4194312, 8388616, 16777224, 33554440, 67108872, 134217736, 268435464, 536870920, 1073741832

Offset: 0

Vincenzo Librandi, May 20 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).

Cf. A000051, A052548, A062709, A140504, A168614, A153972, A168415, A188165.

Magma
```
[2^n+8: n in [0..40]];
```

Table[2^n + 8, {n, 0, 40}] (* or *) CoefficientList[Series[(9 - 17 x)/((1 - x) (1 - 2 x)),{x, 0, 30}], x]
LinearRecurrence[{3,-2},{9,10},40] (* Harvey P. Dale, May 21 2025 *)

G.f.: (9 - 17*x)/((1 - x)*(1 - 2*x)).
a(n) = 2*a(n-1) - 8 = 3*a(n-1) - 2*a(n-2).
a(n) = A052548(n)+6 = A140504(n)+4 = A153972(n)+2.
E.g.f.: exp(2*x) + 8*exp(x). - Elmo R. Oliveira, Nov 11 2023

A246139 a(n) = 2^n + 10.

Original entry on oeis.org

11, 12, 14, 18, 26, 42, 74, 138, 266, 522, 1034, 2058, 4106, 8202, 16394, 32778, 65546, 131082, 262154, 524298, 1048586, 2097162, 4194314, 8388618, 16777226, 33554442, 67108874, 134217738, 268435466, 536870922, 1073741834, 2147483658, 4294967306

Offset: 0

Vincenzo Librandi, Aug 18 2014

First trisection of A085688. [Bruno Berselli, Aug 19 2014]

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).

Cf. Sequences of the form 2^n + k: A000079 (k=0), A000051 (k=1), A052548 (k=2), A062709 (k=3), A140504 (k=4), A168614 (k=5), A153972 (k=6), A168415 (k=7), A242475 (k=8), A188165 (k=9), this sequence (k=10).

Cf. A085688.

Magma
```
[2^n+10: n in [0..40]];
```
Mathematica
```
Table[2^n + 10, {n, 0, 40}]
```

vector(50, n, 2^(n-1)+10) \\ Derek Orr, Aug 18 2014

G.f.: (11 - 21*x)/(1 - 3*x + 2*x^2).
a(n) = A000079(n) + 10.
a(n) = 3*a(n-1) - 2*a(n-2) for n > 1.
E.g.f.: exp(2*x) + 10*exp(x). - Elmo R. Oliveira, Nov 11 2023

A195463 a(n) = 4^(n+1) + 7.

Original entry on oeis.org

11, 23, 71, 263, 1031, 4103, 16391, 65543, 262151, 1048583, 4194311, 16777223, 67108871, 268435463, 1073741831, 4294967303, 17179869191, 68719476743, 274877906951, 1099511627783, 4398046511111, 17592186044423, 70368744177671, 281474976710663, 1125899906842631

Offset: 0

Brad Clardy, Sep 19 2011

These are the even terms of A168415. Since the odd terms of A168415 are divisible by three the primes of this sequence are the same as A104066.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-4).

Cf. A104066, A168415, A188165.

[4^(n+1) + 7: n in [0..30]]; // Vincenzo Librandi, Sep 30 2011

4^Range[25] + 7 (* Paolo Xausa, Feb 21 2025 *)

a(n)=4^(n+1)+7 \\ Charles R Greathouse IV, Sep 19 2011

a(n) = 4^(n+1) + 7.
From Alexander R. Povolotsky, Sep 19 2011: (Start)
G.f.: (11 - 32*x)/(1 - 5*x + 4*x^2).
a(n+1) = 4*a(n) - 21. (End)
a(n) = A188165(2*n+2) - 2. - Bruno Berselli, Sep 26 2011
E.g.f.: exp(x)*(4*exp(3*x) + 7). - Elmo R. Oliveira, Feb 20 2025

A267615 a(n) = 2^n + 11.

Original entry on oeis.org

12, 13, 15, 19, 27, 43, 75, 139, 267, 523, 1035, 2059, 4107, 8203, 16395, 32779, 65547, 131083, 262155, 524299, 1048587, 2097163, 4194315, 8388619, 16777227, 33554443, 67108875, 134217739, 268435467, 536870923, 1073741835, 2147483659, 4294967307, 8589934603, 17179869195, 34359738379

Offset: 0

Ilya Gutkovskiy, Jan 18 2016

Recurrence relation b(n) = 3*b(n - 1) - 2*b(n - 2) for n>1, b(0) = k, b(1) = k + 1, gives the closed form b(n) = 2^n + k - 1.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Cf. sequences with closed form 2^n + k - 1: A168616 (k=-4), A028399 (k=-3), A036563 (k=-2), A000918 (k=-1), A000225 (k=0), A000079 (k=1), A000051 (k=2), A052548 (k=3), A062709 (k=4), A140504 (k=5), A168614 (k=6), A153972 (k=7), A168415 (k=8), A242475 (k=9), A188165 (k=10), A246139 (k=11), this sequence (k=12).

Cf. A156940.

[2^n+11: n in [0..30]]; // Vincenzo Librandi, Jan 19 2016

Table[2^n + 11, {n, 0, 35}]
LinearRecurrence[{3, -2}, {12, 13}, 40] (* Vincenzo Librandi, Jan 19 2016 *)

a(n) = 2^n + 11; \\ Altug Alkan, Jan 18 2016

G.f.: (12 - 23*x)/(1 - 3*x + 2*x^2).
a(n) = 3*a(n - 1) - 2*a(n - 2) for n>1, a(0)=12, a(1)=13.
a(n) = A000079(n) + A010850(n).
Sum_{n>=0} 1/a(n) = 0.367971714327125...
Lim_{n->oo} a(n + 1)/a(n) = 2.
E.g.f.: exp(2*x) + 11*exp(x). - Elmo R. Oliveira, Nov 08 2023

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A240942 Numbers k that divide 2^k + 9.

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A242475 a(n) = 2^n + 8.

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A246139 a(n) = 2^n + 10.

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A195463 a(n) = 4^(n+1) + 7.

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A267615 a(n) = 2^n + 11.

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