A074602 -id:A074602 - cp's OEIS frontend

A155590 a(n) = 7^n + 2^n - 1.

1, 8, 52, 350, 2416, 16838, 117712, 823670, 5765056, 40354118, 282476272, 1977328790, 13841291296, 96889018598, 678223089232, 4747561542710, 33232930635136, 232630514118278, 1628413598172592, 11398895185897430, 79792266298660576, 558545864085381158, 3909821048587182352

Offset: 0

Mohammad K. Azarian, Jan 24 2009

Paolo Xausa, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-23,14).

Cf. A074501, A074600, A005057, A005056, A099393, A155588, A155590.

Table[7^n + 2^n - 1, {n, 0, 25}] (* Paolo Xausa, Jul 30 2024 *)

a(n)=7^n+2^n-1 \\ Charles R Greathouse IV, Sep 24 2015

G.f.: 1/(1-7*x)+1/(1-2*x)-1/(1-x).
E.g.f.: exp(7*x)+exp(2*x)-exp(x).
a(n) = 9*a(n-1)-14*a(n-2)-6 with a(0) = 1, a(1) = 8. - Vincenzo Librandi, Jul 21 2010
a(n) = A074602(n)-1. - R. J. Mathar, Mar 10 2022

A176946 Primes of the form 7^k+2^k.

Original entry on oeis.org

2, 53, 2417

Offset: 1

Vincenzo Librandi, Apr 29 2010

If 7^k+2^k is prime then k is either 0 or a power of 2. The corresponding values of k for a(1)-a(3) are 0, 2 and 4. If it exists, a(4) has k = 2^m with m > 19, and therefore it is larger than 7^(2^20) > 10^886149. - Amiram Eldar, Jul 17 2025

Primes in A074602.

[ a: k in [0..2100] | IsPrime(a) where a is 7^k+2^k ];

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

Original entry on oeis.org

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).

A045580 Numbers k that divide 7^k + 2^k.

Original entry on oeis.org

1, 3, 9, 27, 39, 81, 117, 171, 243, 351, 507, 513, 729, 1053, 1521, 1539, 2187, 2223, 3081, 3159, 3249, 4563, 4617, 5109, 6123, 6561, 6591, 6669, 9243, 9477, 9747, 13689, 13851, 15327, 18153, 18369, 19683, 19773, 20007, 27729, 28431, 28899, 29241, 39159, 40053

Offset: 1

David W. Wilson

nonn

Amiram Eldar, Table of n, a(n) for n = 1..2000

Cf. A074602.

Select[Range[30000], Divisible[PowerMod[2, #, #] + PowerMod[7, #, #], #] &] (* Amiram Eldar, Oct 23 2021 *)

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A155590 a(n) = 7^n + 2^n - 1.

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A176946 Primes of the form 7^k+2^k.

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Magma

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

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Magma

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A045580 Numbers k that divide 7^k + 2^k.

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Mathematica