A074610 -id:A074610 - cp's OEIS frontend

A245806 a(n) = 3^n + 10^n.

2, 13, 109, 1027, 10081, 100243, 1000729, 10002187, 100006561, 1000019683, 10000059049, 100000177147, 1000000531441, 10000001594323, 100000004782969, 1000000014348907, 10000000043046721, 100000000129140163, 1000000000387420489, 10000000001162261467

Offset: 0

Vincenzo Librandi, Aug 04 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (13,-30).

Cf. 3^n+k^n: A034472 (k=1), A007689 (k=2), A008776 (k=3), A074605 (k=4), A074606 (k=5), A074607 (k=6), A074608 (k=7), A074609 (k=8), A074610 (k=9), this sequence (k=10).

Magma
```
[3^n+10^n: n in [0..25]];
```

I:=[2,13]; [n le 2 select I[n] else 13*Self(n-1)-30*Self(n-2): n in [1..25]];

Table[(3^n + 10^n), {n, 0, 30}] (* or *) CoefficientList[Series[(2 - 13 x)/((1 - 3 x) (1 - 10 x)), {x, 0, 30}], x]

a(n)=3^n + 10^n \\ Charles R Greathouse IV, Aug 26 2014

G.f.: (2-13*x)/((1-3*x)(1-10*x)).
E.g.f.: e^(3*x) + e^(10*x).
a(n) = 13*a(n-1)-30*a(n-2) for n>1.
a(n) = A000244(n) + A011557(n). - Michel Marcus, Aug 04 2014

A045588 Numbers k that divide 9^k + 3^k.

Original entry on oeis.org

1, 2, 3, 6, 9, 10, 18, 21, 27, 30, 50, 54, 63, 81, 90, 147, 150, 162, 171, 189, 243, 250, 270, 333, 438, 441, 450, 486, 513, 567, 729, 750, 810, 903, 999, 1029, 1197, 1250, 1314, 1323, 1350, 1458, 1539, 1701, 2187, 2190, 2250, 2331, 2430, 2709, 2997, 3087

Offset: 1

David W. Wilson

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A074610.

Select[Range[3100],Divisible[9^#+3^#,#]&] (* Harvey P. Dale, Aug 13 2015 *)
Select[Range[300], Divisible[PowerMod[9, #, #] + PowerMod[3, #, #], #] &] (* Amiram Eldar, Oct 23 2021 *)

cp's OEIS Frontend

A245806 a(n) = 3^n + 10^n.

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