A059802
Numbers k such that 5^k - 4^k is prime.
Original entry on oeis.org
3, 43, 59, 191, 223, 349, 563, 709, 743, 1663, 5471, 17707, 19609, 35449, 36697, 45259, 91493, 246497, 265007, 289937
Offset: 1
New term 246497 found by Jean-Louis Charton in 2008 corresponding to a probable prime with 172295 digits -
Jean-Louis Charton, Sep 02 2009
A062572
Numbers k such that 6^k - 5^k is prime.
Original entry on oeis.org
2, 5, 11, 13, 23, 61, 83, 421, 1039, 1511, 31237, 60413, 113177, 135647, 258413
Offset: 1
2 is in the sequence because 6^2 - 5^2 = 36 - 25 = 11, which is prime.
3 is not in the sequence because 6^3 - 5^3 = 216 - 125 = 91 = 7 * 13, which is not prime.
Two more terms (31237 and 60413) found by Predrag Minovic in 2004 corresponding to probable primes with 24308 and 47011 digits.
Jean-Louis Charton, Oct 06 2010
Two more terms (113177 and 135647) found by Jean-Louis Charton in 2009 corresponding to probable primes with 88069 and 105554 digits.
Jean-Louis Charton, Oct 13 2010
A062666
Numbers k such that 100^k - 99^k is prime.
Original entry on oeis.org
2, 5, 19, 59, 1013, 2371, 13967, 44683
Offset: 1
-
lst={}; k=100; Do[If[PrimeQ[k^n-(k-1)^n], Print[n]; AppendTo[lst, n]], {n, 10^5}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 26 2008 *)
-
forprime(p=2,1e5,if(ispseudoprime(100^p-99^p),print1(p", "))) \\ Charles R Greathouse IV, Jun 10 2011
A062589
Numbers k such that 23^k - 22^k is prime, or a strong pseudoprime.
Original entry on oeis.org
229, 241, 673, 5387, 47581
Offset: 1
A062587
Numbers k such that 21^k - 20^k is prime.
Original entry on oeis.org
2, 19, 41, 43, 337, 479, 9127, 37549, 44017, 59971, 128327, 176191, 193601
Offset: 1
A128027
Numbers n such that (11^n - 3^n)/8 is prime.
Original entry on oeis.org
3, 5, 19, 31, 367, 389, 431, 2179, 10667, 13103, 90397
Offset: 1
-
[p: p in PrimesUpTo(400) | IsPrime((11^p-3^p) div 8)]; // Vincenzo Librandi, Nov 20 2014
-
A128027:=n->`if`(isprime((11^n-3^n)/8),n,NULL): seq(A128027(n),n=1..1000); # Wesley Ivan Hurt, Nov 19 2014
-
k=8; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]
Do[If[PrimeQ[(11^n - 3^n)/8], Print[n]], {n, 10^4}] (* Ryan Propper, Mar 17 2007 *)
Select[Prime[Range[1200]], PrimeQ[(11^# - 3^#)/8] &] (* Vincenzo Librandi, Nov 20 2014 *)
-
is(n)=ispseudoprime((11^n - 3^n)/8) \\ Charles R Greathouse IV, Feb 17 2017
A128024
Numbers k such that (7^k - 3^k)/4 is prime.
Original entry on oeis.org
3, 7, 19, 109, 131, 607, 863, 2917, 5923, 12421, 187507, 353501, 817519
Offset: 1
-
k=4; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]
-
forprime(p=3,1e5,if(ispseudoprime((7^p-3^p)/4),print1(p", "))) \\ Charles R Greathouse IV, Jun 01 2011
-
from sympy import isprime
def aupto(lim): return [k for k in range(lim+1) if isprime((7**k-3**k)//4)]
print(aupto(900)) # Michael S. Branicky, Mar 07 2021
A128026
Numbers n such that (10^n - 3^n)/7 is prime.
Original entry on oeis.org
2, 3, 5, 37, 599, 38393, 51431, 118681, 376417
Offset: 1
Cf.
A028491 = numbers n such that (3^n - 1)/2 is prime.
Cf.
A057468 = numbers n such that 3^n - 2^n is prime.
Cf.
A059801 = numbers n such that 4^n - 3^n is prime.
Cf.
A121877 = numbers n such that (5^n - 3^n)/2 is a prime.
-
k=7; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]
-
forprime(p=2,1e4,if(ispseudoprime((10^p-3^p)/7),print1(p", "))) \\ Charles R Greathouse IV, Jun 05 2011
A128028
Numbers k such that (13^k - 3^k)/10 is prime.
Original entry on oeis.org
7, 31, 41, 269, 283, 7333, 8803
Offset: 1
-
k=10; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]
-
is(n)=isprime((13^n-3^n)/10) \\ Charles R Greathouse IV, Feb 17 2017
A128025
Numbers k such that (8^k - 3^k)/5 is prime.
Original entry on oeis.org
2, 3, 7, 19, 31, 67, 89, 9227, 43891, 854149
Offset: 1
-
k=5; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]
-
is(n)=isprime((8^n-3^n)/5) \\ Charles R Greathouse IV, Feb 17 2017
Showing 1-10 of 122 results.
Comments