A074613 -id:A074613 - cp's OEIS frontend

A245807 a(n) = 7^n + 10^n.

2, 17, 149, 1343, 12401, 116807, 1117649, 10823543, 105764801, 1040353607, 10282475249, 101977326743, 1013841287201, 10096889010407, 100678223072849, 1004747561509943, 10033232930569601, 100232630513987207, 1001628413597910449, 10011398895185373143

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 (17,-70).

Cf. 7^n+k^n: A034491 (k=1), A074602 (k=2), A074608 (k=3), A074613 (k=4), A074616 (k=5), A074619 (k=6), A109808 (k=7), A074622 (k=8), A074623 (k=9), this sequence (k=10).

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

I:=[2,17]; [n le 2 select I[n] else 17*Self(n-1)-70*Self(n-2): n in [1..25]];

Table[(7^n + 10^n), {n, 0, 30}] (* or *) CoefficientList[Series[(2 - 17 x)/((1 - 7 x) (1 - 10 x)), {x, 0, 40}], x]

G.f.: (2-17*x)/((1-7*x)*(1-10*x)).
E.g.f.: e^(7*x) + e^(10*x).
a(n) = 17*a(n-1)-70*a(n-2).
a(n) = A000420(n) + A011557(n).

A045592 Numbers k that divide 7^k + 4^k.

Original entry on oeis.org

1, 11, 121, 253, 737, 1331, 2783, 5819, 8107, 14641, 16951, 30613, 49379, 64009, 89177, 116897, 133837, 161051, 186461, 336743, 389873, 543169, 640343, 704099, 980947, 1135717, 1285867, 1292071, 1472207, 1771561, 2051071, 2688631

Offset: 1

David W. Wilson

nonn

Cf. A074613.

Select[Range[269*10^4],Mod[PowerMod[7,#,#]+PowerMod[4,#,#],#]==0&] (* Harvey P. Dale, Jun 25 2021 *)

cp's OEIS Frontend

A245807 a(n) = 7^n + 10^n.

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