A051440 -id:A051440 - cp's OEIS frontend

A033844 a(n) = prime(2^n).

2, 3, 7, 19, 53, 131, 311, 719, 1619, 3671, 8161, 17863, 38873, 84017, 180503, 386093, 821641, 1742537, 3681131, 7754077, 16290047, 34136029, 71378569, 148948139, 310248241, 645155197, 1339484197, 2777105129, 5750079047, 11891268401, 24563311309, 50685770167, 104484802057, 215187847711

Offset: 0

Vasiliy Danilov (danilovv(AT)usa.net), Jun 15 1998

a(n) is the smallest number m such that pi(m)=d(m)^n, where d(m) is number of positive divisors of m (the proof is easy). - Farideh Firoozbakht, Jun 06 2005

David Baugh, Table of n, a(n) for n = 0..78 (terms n = 0..57 from Charles R Greathouse IV, terms n = 58..78 found using Kim Walisch's primecount program).

Cf. A000040, A018249, A051438, A051440, A051439, A006988, A107655.

Mathematica
```
Table[Prime[2^n], {n, 0, 32}]
```

a(n)=prime(2^n) \\ Charles R Greathouse IV, Nov 02 2014

More terms from Robert G. Wilson v, Jun 09 2000

A051439 a(n) = prime(2^n + 1).

Original entry on oeis.org

3, 5, 11, 23, 59, 137, 313, 727, 1621, 3673, 8167, 17881, 38891, 84047, 180511, 386117, 821647, 1742539, 3681149, 7754081, 16290073, 34136059, 71378603, 148948141, 310248251, 645155227, 1339484207, 2777105131, 5750079077

Offset: 0

N. J. A. Sloane

nonn

			a(0) = prime(2^0+1) = prime(2) = 3,
a(1) = prime(2+1) = prime(3) = 5,
a(2) = prime(2^2+1) = prime(5) = 11,
a(3) = prime(2^3+1) = prime(9) = 23, and so on. - _N. J. A. Sloane_, Dec 09 2020

Hugo Pfoertner, Table of n, a(n) for n = 0..78, using David Baugh's b-file from A033844.
Kim Walisch, Fast C++ prime counting function implementation.

Cf. A000040, A033844, A018249, A051438, A051440.

Prime[2^Range[0,30]+1] (* Harvey P. Dale, Jan 19 2014 *)

More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999

A051438 a(n) = prime(2^n - 1).

Original entry on oeis.org

2, 5, 17, 47, 127, 307, 709, 1613, 3659, 8147, 17851, 38867, 84011, 180497, 386083, 821603, 1742527, 3681113, 7754017, 16290041, 34136021, 71378551, 148948133, 310248233, 645155191, 1339484149, 2777105117, 5750079043, 11891268397, 24563311217, 50685770143

Offset: 1

N. J. A. Sloane

nonn

Amiram Eldar, Table of n, a(n) for n = 1..78 (calculated using the b-file at A033844; terms 1..57 from Hugo Pfoertner)

Cf. A000040, A000225, A033844, A018249, A051440, A051439, A151799.

Prime[2^Range[34] - 1] (* Vladimir Joseph Stephan Orlovsky, Jul 19 2011 *)

a(n)=prime(2^n-1) \\ Charles R Greathouse IV, Sep 28 2015

a(n) = A181363(2^n - 1). - Reinhard Zumkeller, Oct 16 2010
a(n) = A000040(A000225(n)). - Michel Marcus, Nov 28 2017
a(n) = A151799(A033844(n)). - Amiram Eldar, Jun 30 2024

More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999

A018249 a(n) = prime(2^n)-1.

Original entry on oeis.org

1, 2, 6, 18, 52, 130, 310, 718, 1618, 3670, 8160, 17862, 38872, 84016, 180502, 386092, 821640, 1742536, 3681130, 7754076, 16290046, 34136028, 71378568, 148948138, 310248240, 645155196, 1339484196, 2777105128, 5750079046, 11891268400, 24563311308, 50685770166, 104484802056

Offset: 0

N. J. A. Sloane

nonn

Amiram Eldar, Table of n, a(n) for n = 0..78
Paul Cooijmans, Numbers, Item 18, 1995.
Paul Cooijmans, Short Test For Genius, Item 29, 2002.

Cf. A000040, A033844, A051438, A051440, A051439.

Prime[2^Range[0,30]]-1 (* Harvey P. Dale, Sep 30 2016 *)

a(n) = prime(2^n) - 1; \\ Amiram Eldar, Jul 11 2025

a(n) = A033844(n) - 1.

a(n) = A051440(n) - 2. - Amiram Eldar, Jul 11 2025

More terms from Amiram Eldar, Jul 11 2025

cp's OEIS Frontend

A033844 a(n) = prime(2^n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A051439 a(n) = prime(2^n + 1).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A051438 a(n) = prime(2^n - 1).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A018249 a(n) = prime(2^n)-1.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions