A075081 -id:A075081 - cp's OEIS frontend

A076481 Primes of the form (3^n-1)/2.

13, 1093, 797161, 3754733257489862401973357979128773, 6957596529882152968992225251835887181478451547013

Offset: 1

Dean Hickerson, Oct 14 2002

nonn

All primes p whose reciprocals belong to the middle-third Cantor set satisfy an equation of the form 2pK + 1 = 3^n. This sequence is the special case K = 1. See reference. [Christian Salas, Jul 04 2011]

Conjecture: primes p such that sigma(2p+1) = 3*p+1. Sigma(2*a(n)+1) = 3*a(n) +1 holds for all first 9 terms. - Jaroslav Krizek, Sep 28 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..9
Christian Salas, On prime reciprocals in the Cantor set, arXiv:0906.0465v5 [math.NT], 2009-2011.
Christian Salas, Cantor primes as prime-valued cyclotomic polynomials, arXiv preprint arXiv:1203.3969 [math.NT], 2012.

The exponents n are in A028491. Cf. A075081.

[a: n in [1..200] | IsPrime(a) where a is (3^n-1) div 2 ]; // Vincenzo Librandi, Dec 09 2011

A076481:=n->`if`(isprime((3^n-1)/2), (3^n-1)/2, NULL): seq(A076481(n), n=1..100); # Wesley Ivan Hurt, Sep 30 2014

Select[Table[(3^n-1)/2, {n,0,500}], PrimeQ] (* Vincenzo Librandi, Dec 09 2011 *)

for(n=3,99,if(ispseudoprime(t=3^n\2),print1(t", "))) \\ Charles R Greathouse IV, Jul 02 2013

A308150 Numbers k such that sigma(k) mod k is prime, where sigma = A000203.

Original entry on oeis.org

4, 8, 18, 20, 21, 27, 32, 35, 36, 39, 50, 55, 57, 63, 65, 77, 85, 98, 100, 104, 111, 115, 125, 128, 129, 155, 161, 171, 175, 185, 187, 189, 196, 201, 203, 205, 209, 221, 235, 237, 242, 245, 265, 275, 279, 291, 299, 305, 309, 319, 323, 324, 325, 327, 335, 338, 341, 365, 371, 377, 381, 385, 391

Offset: 1

J. M. Bergot and Robert Israel, May 14 2019

nonn

Includes 1+A000668.

			a(3) = 18 is in the sequence because sigma(18) = 39, 39 == 3 (mod 18), and 3 is prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000203, A000668, A054024.

Includes A037020 and A075081.

select(n -> isprime(numtheory:-sigma(n) mod n), [$2..1000]);

isok(n) = isprime(sigma(n) % n); \\ Michel Marcus, May 15 2019

A075079 Numbers k in A001597 such that 2*k + 1 is prime.

Original entry on oeis.org

1, 8, 9, 36, 81, 125, 128, 216, 243, 441, 576, 729, 900, 1089, 1296, 1331, 1728, 1764, 2025, 4356, 5184, 5625, 7569, 8000, 8649, 9216, 9261, 9801, 10404, 11025, 15129, 17424, 17576, 18225, 19683, 23409, 24336, 24389, 26244, 27000, 31329, 32768, 34596, 35721

Offset: 1

Zak Seidov, Oct 11 2002

			2*8 + 1 = 17 is prime, so 8 is a term.

Cf. A001597, A075081.

lista(nn) = {vec = vector(nn, i, i); pp = select(i->((ispower(i) || (i==1)) && isprime(2*i+1)), vec); for (i = 1, #pp, print1(pp[i], ", "));} \\ Michel Marcus, Oct 02 2013

More terms from Michel Marcus, Oct 02 2013

A096723 Numbers n such that 3^n has the form 2p-+1 where p is prime.

Original entry on oeis.org

1, 2, 3, 4, 7, 13, 16, 32, 64, 71, 103, 541, 1091, 1367, 1627, 4177, 9011, 9551, 36913, 43063, 49681, 57917, 483611, 877843, 2215303, 2704981, 3598867

Offset: 1

Lekraj Beedassy, Jul 05 2004

For the corresponding primes p see A088553.

For n > 1, numbers n such that (3^n + (-1)^n)/2 is prime. - Thomas Ordowski, Dec 26 2016

Cf. A028491, A075081, A088553, A093625, A171381.

Select[Range[4200],Or@@PrimeQ[(3^#+{1,-1})/2]&] (* Harvey P. Dale, Mar 05 2013 *)

More terms from Ray Chandler, Jul 09 2004

a(25)-a(27) (from A028491 and A171381) from Tyler Busby, Mar 22 2023

A172095 Integers k such that k-1,k,k+1 have few distinct primes: k=p^r, p odd prime, and (k^2-1)/8 divisible by at most two distinct prime factors.

Original entry on oeis.org

3, 5, 7, 9, 11, 13, 17, 19, 27, 37, 53, 107, 163, 243, 2187, 2917, 4373, 8747, 1594323, 86093443

Offset: 1

Dino Lorenzini (lorenzin(AT)uga.edu), Jan 25 2010

Note the terms 3^1=3, 3^2=9, 3^3=27, 3^5=243, 3^7=2187, and 3^13=1594323. The other listed terms are prime.

Next term > 2^2000. - Max Alekseyev, Feb 16 2011

Cf. A075081, A062547, A111974, A005105

Edited and missing terms 3, 5, 9, 17 added by Max Alekseyev, Feb 16 2011

cp's OEIS Frontend

A076481 Primes of the form (3^n-1)/2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

A308150 Numbers k such that sigma(k) mod k is prime, where sigma = A000203.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

PARI

A075079 Numbers k in A001597 such that 2*k + 1 is prime.

Views

Author

Keywords

Examples

Crossrefs

Programs

PARI

Extensions

A096723 Numbers n such that 3^n has the form 2p-+1 where p is prime.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Extensions

A172095 Integers k such that k-1,k,k+1 have few distinct primes: k=p^r, p odd prime, and (k^2-1)/8 divisible by at most two distinct prime factors.

Views

Author

Keywords

Comments

Crossrefs

Extensions