A023265 -id:A023265 - cp's OEIS frontend

A023296 Primes that remain prime through 3 iterations of function f(x) = 9x + 2.

19, 103, 113, 151, 239, 283, 313, 599, 929, 1481, 2411, 2549, 2593, 2741, 2819, 2969, 3931, 4091, 4463, 4523, 5279, 5923, 6781, 7759, 8209, 8363, 9749, 10133, 10531, 12919, 14071, 15053, 15361, 16229, 16453, 16493, 16573, 16703, 17041, 17783, 18253

Offset: 1

David W. Wilson

nonn

Primes p such that 9*p+2, 81*p+20 and 729*p+182 are also primes. - Vincenzo Librandi, Aug 04 2010

John Cerkan, Table of n, a(n) for n = 1..10000

Subsequence of A023233 and A023265.

[n: n in [1..450000] | IsPrime(n) and IsPrime(9*n+2) and IsPrime(81*n+20) and IsPrime(729*n+182)]; // Vincenzo Librandi, Aug 04 2010

A023296:=n->`if`(isprime(n) and isprime(9*n+2) and isprime(81*n+20) and isprime(729*n+182), n, NULL): seq(A023296(n), n=1..5*10^4); # Wesley Ivan Hurt, Feb 22 2017

Select[Prime@ Range@ 2100, Times @@ Boole@ PrimeQ@ NestList[9 # + 2 &, #, 3] > 0 &] (* Michael De Vlieger, Feb 22 2017 *)
Select[Prime[Range[2100]],AllTrue[Rest[NestList[9#+2&,#,3]],PrimeQ]&] (* Harvey P. Dale, May 14 2024 *)

A086154 a(n) = binomial(3^n,2^n).

Original entry on oeis.org

1, 3, 126, 2220075, 33594090947249085, 9812294412288780842726471233974791140221, 747581321238203931168470352555568799370148397202082975882483140118428447896681620077224288595

Offset: 0

Labos Elemer, Aug 07 2003

nonn

Upper bound on the number of compressed (irredundant) disjunctive normal forms of Boolean functions with n variables.

G. P. Gavrilov and A. A. Saposhenko, Problems Book in Discrete Mathematics (Hungarian translation), Muszaki Kiado, 1981.

Amiram Eldar, Table of n, a(n) for n = 0..8

Cf. A023265.

[Binomial(3^n,2^n) : n in [0..7]]; // Wesley Ivan Hurt, Apr 20 2021

Mathematica
```
Table[Binomial[3^w, 2^w], {w, 0, 5}]
```

a(n)=binomial(3^n,2^n) \\ Charles R Greathouse IV, Dec 19 2011

A023352 Primes that remain prime through 5 iterations of function f(x) = 9x + 2.

Original entry on oeis.org

103, 283, 929, 3931, 7759, 52973, 75853, 90031, 93371, 103561, 106949, 110821, 128111, 130841, 137273, 163861, 198553, 288023, 342389, 357031, 377231, 425681, 429973, 435181, 450311, 490663, 526159, 532199, 552791, 574801, 585733, 599719

Offset: 1

David W. Wilson

nonn

Primes p such that 9*p+2, 81*p+20, 729*p+182, 6561*p+1640 and 59049*p+14762 are also primes. - Vincenzo Librandi, Aug 05 2010

John Cerkan, Table of n, a(n) for n = 1..10000

Subsequence of A023233, A023265, A023296, and A023324.

[n: n in [1..19000000] | IsPrime(n) and IsPrime(9*n+2) and IsPrime(81*n+20) and IsPrime(729*n+182) and IsPrime(6561*n+1640) and IsPrime(59049*n+14762)] // Vincenzo Librandi, Aug 05 2010

Select[Prime[Range[50000]],AllTrue[Rest[NestList[9#+2&,#,5]],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 24 2017 *)

cp's OEIS Frontend

A023296 Primes that remain prime through 3 iterations of function f(x) = 9x + 2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

A086154 a(n) = binomial(3^n,2^n).

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A023352 Primes that remain prime through 5 iterations of function f(x) = 9x + 2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica