A299383
Numbers k such that k * 20^k - 1 is prime.
Original entry on oeis.org
1, 18, 44, 60, 80, 123, 429, 1166, 2065, 8774, 35340, 42968, 50312, 210129
Offset: 1
Numbers n such that n * b^n - 1 is prime:
A008864 (b=1),
A002234 (b=2),
A006553 (b=3),
A086661 (b=4),
A059676 (b=5),
A059675 (b=6),
A242200 (b=7),
A242201 (b=8),
A242202 (b=9),
A059671 (b=10),
A299374 (b=11),
A299375 (b=12),
A299376 (b=13),
A299377 (b=14),
A299378 (b=15),
A299379 (b=16),
A299380 (b=17),
A299381 (b=18),
A299382 (b=19), this sequence (b=20).
-
[n: n in [1..10000] |IsPrime(n*20^n-1)];
-
Select[Range[1, 10000], PrimeQ[n*20^n-1] &]
-
for(n=1, 10000, if(isprime(n*20^n-1), print1(n", ")))
A210340
Generalized Woodall primes: any primes that can be written in the form n*b^n - 1 with n+2 > b > 2.
Original entry on oeis.org
17, 191, 4373, 5119, 524287, 590489, 3124999, 14680063, 3758096383, 6973568801, 34867844009, 85449218749, 824633720831, 1099999999999, 1618481116086271, 11577835060199423, 14999999999999999, 29311444762388081, 73123168801259519
Offset: 1
167*2^668 - 1 is a prime number and 167*2^668 - 1 = 167*16^167 - 1, so this number is in the sequence.
- Arkadiusz Wesolowski, Table of n, a(n) for n = 1..170
- Chris Caldwell, The Top 20 Generalized Woodall Primes
- Chris Caldwell, The Prime Glossary, Woodall prime
- G. L. Honaker, Jr. and Chris Caldwell, 17962...40287 (1006-digits)
- G. L. Honaker, Jr. and Chris Caldwell, 19981...99999 (10028-digits)
- PrimeGrid, Home Page
- Wikipedia, Woodall number
-
lst = {}; Do[p = n*b^n - 1; If[p < 10^200 && PrimeQ[p], AppendTo[lst, p]], {b, 3, 100}, {n, b - 1, 413}]; Sort@lst
A242336
Numbers k such that k*5^k-1 is semiprime.
Original entry on oeis.org
1, 2, 6, 12, 15, 19, 20, 26, 50, 55, 66, 68, 96, 99, 150, 166, 228, 459
Offset: 1
Cf. similar sequences listed in
A242273.
-
IsSemiprime:=func; [n: n in [1..400] | IsSemiprime(s) where s is n*5^n-1];
-
select(t -> (numtheory:-bigomega(t*5^t-1)=2), [$1..400]); # Robert Israel, Aug 18 2015
-
Select[Range[400], PrimeOmega[# 5^# - 1]==2&]
Comments