A121824 -id:A121824 - cp's OEIS frontend

A121877 Numbers k such that (5^k - 3^k)/2 = A005059(k) is prime.

13, 19, 23, 31, 47, 127, 223, 281, 2083, 5281, 7411, 7433, 19051, 27239, 35863, 70327, 128941, 147571, 182099, 866029

Offset: 1

Alexander Adamchuk, Aug 31 2006, Oct 08 2006

All terms are primes. Their indices are listed in A123704.
Corresponding primes are listed in A123705.
If it exists, a(17) > 125000. - Robert Price, Aug 15 2011
If it exists, a(21) > 1000000. - Jon Grantham, Jul 29 2023

OEIS Wiki, Primes of the form (a^n+b^n)/(a+b) and (a^n-b^n)/(a-b).
Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.

Cf. A005058, A005059, A109347, A120612, A081186, A121824, A123704, A123705.

Do[f=(5^n-3^n)/2;If[PrimeQ[f],Print[{n,f}]],{n,1,300}]

forprime(p=2,1e4,if(ispseudoprime((5^p-3^p)>>1),print1(p", "))) \\ Charles R Greathouse IV, Jun 16 2011

a(n) = prime(A123704(n)).

More terms from Farideh Firoozbakht, Oct 11 2006
a(13)-a(16) from Robert Price, Aug 15 2011
a(17)-a(19) from Kellen Shenton, May 18 2022
a(20) from Jon Grantham, Jul 29 2023

A122853 Numbers k such that (3^k + 5^k)/8 = A074606(k)/8 is a prime.

Original entry on oeis.org

3, 5, 7, 17, 19, 109, 509, 661, 709, 1231, 12889, 13043, 26723, 43963, 44789

Offset: 1

Alexander Adamchuk, Sep 14 2006

(3^k + 5^k)/8 = A074606(k)/8 = A081186(k)/4.
Corresponding primes of the form (3^k + 5^k)/2^3 are listed in {A121938(n)} = {A079773(a(n))} = {19, 421, 10039, 95383574161, 2384331073699, ...}.
No other terms less than 100000. - Robert Price, Apr 28 2012

Cf. A074606, A081186, A121824, A121877, A005058, A005059, A121938, A109347, A079773.

Do[f=5^n+3^n;If[PrimeQ[f/2^3],Print[{n,f/2^3}]],{n,1,1231}]

select(n->isprime((3^n + 5^n)/8), vector(2000,i,i)) \\ Charles R Greathouse IV, Feb 13 2011

a(11)-a(15) from Robert Price, Apr 28 2012

A121938 Primes of the form (3^k + 5^k)/2^3 = A074606(k)/8.

Original entry on oeis.org

19, 421, 10039, 95383574161, 2384331073699, 1925929944387235853055979210606894889560480247048440342330377620014353281101

Offset: 1

Zak Seidov, Sep 10 2006

Corresponding numbers k such that (3^k + 5^k)/8 is prime are listed in A122853. All these numbers are primes. - Alexander Adamchuk, Sep 14 2006

The next term is too large to include. - Alexander Adamchuk, Sep 14 2006

Cf. A074706, A122853, A081186, A079773, A121824, A121877, A005058, A005059, A121938, A109347.

Do[f=5^n+3^n;If[PrimeQ[f/2^3],Print[{n,f/2^3}]],{n,1,1231}] (* Alexander Adamchuk, Sep 14 2006 *)

a(n) = (A122853(n)^3 + A122853(n)^5)/8. a(n) = A074606[A122853(n)]/8 = A081186[A122853(n)]/4. a(n) = A079773[A122853(n)]. - Alexander Adamchuk, Sep 14 2006

More terms from Alexander Adamchuk, Sep 14 2006

cp's OEIS Frontend

A121877 Numbers k such that (5^k - 3^k)/2 = A005059(k) is prime.

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A122853 Numbers k such that (3^k + 5^k)/8 = A074606(k)/8 is a prime.

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A121938 Primes of the form (3^k + 5^k)/2^3 = A074606(k)/8.

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