A155603 -id:A155603 - cp's OEIS frontend

A155615 a(n) = 10^n - 3^n + 1.

1, 8, 92, 974, 9920, 99758, 999272, 9997814, 99993440, 999980318, 9999940952, 99999822854, 999999468560, 9999998405678, 99999995217032, 999999985651094, 9999999956953280, 99999999870859838, 999999999612579512

Offset: 0

Mohammad K. Azarian, Jan 26 2009

Index entries for linear recurrences with constant coefficients, signature (14,-43,30).

Cf. A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606, A155607, A155608, A155609, A155610, A155611, A155612, A155613, A155614.

a(n)=10^n-3^n+1 \\ Charles R Greathouse IV, Oct 07 2015

G.f.: 1/(1-10*x)-1/(1-3*x)+1/(1-x).
E.g.f.: e^(10*x)-e^(3*x)+e^x.
a(n) = 13*a(n-1)-30*a(n-2)+18 with a(0)=1, a(1)=8. - Vincenzo Librandi, Jul 21 2010

A180741 Numbers k such that 5^k + 3^k - 1 is prime.

Original entry on oeis.org

1, 3, 9, 39, 165, 11289, 44979, 192321, 377865

Offset: 1

Vincenzo Librandi, Jan 22 2011

No additional terms up to 5000. - Harvey P. Dale, Feb 01 2011

No additional terms up to 1000000. - Jon Grantham, Jul 29 2023

Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.

Cf. A155603.

Magma
```
[n: n in [0..1000]|IsPrime(5^n+3^n-1)]
```

Select[Range[5000],PrimeQ[5^#+3^#-1]&]  (* Harvey P. Dale, Feb 01 2011 *)

is(n)=ispseudoprime(5^n+3^n-1) \\ Charles R Greathouse IV, Jun 13 2017

from sympy import isprime
def afind(limit, startk=1):
    pow5, pow3 = 5**startk, 3**startk
    for k in range(startk, limit+1):
        if isprime(pow5 + pow3 - 1): print(k, end=", ")
        pow5 *= 5; pow3 *= 3
afind(1000) # Michael S. Branicky, Aug 21 2021

a(6) from Michael S. Branicky, Aug 21 2021
a(7) from Michael S. Branicky, May 13 2023
a(8), a(9) from Jon Grantham, Jul 29 2023

A277122 Primes of the form 5^k + 3^k - 1.

Original entry on oeis.org

7, 151, 1972807, 1818989407598411628849054391, 21382117680737565169124291737211855035830505403680318251383549467509816267540836044857784735512271804718726595516967

Offset: 1

Alex Ratushnyak, Sep 30 2016

nonn

The sequence of corresponding k starts: 1, 3, 9, 39, 165 (A180741).

Primes in A155603. - Altug Alkan, Oct 01 2016

Cf. A000040, A081508, A155603, A180741.

Select[Table[5^k + 3^k - 1, {k, 0, 200}], PrimeQ] (* Amiram Eldar, Aug 11 2024 *)

lista(kmax) = {my(p); for(k = 0, kmax, p = 5^k + 3^k - 1; if(isprime(p), print1(p, ", ")));} \\ Amiram Eldar, Aug 11 2024

a(n) = A155603(A180741(n)). - Amiram Eldar, Aug 11 2024

cp's OEIS Frontend

A155615 a(n) = 10^n - 3^n + 1.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A180741 Numbers k such that 5^k + 3^k - 1 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Python

Extensions

A277122 Primes of the form 5^k + 3^k - 1.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

PARI

Formula