A110931
Numbers k such that 2*k^k - 1 is prime.
Original entry on oeis.org
2, 3, 357, 1400, 205731, 296598
Offset: 1
3 is in the sequence since 2*3^3 - 1 = 53 is prime.
Numbers k such that b*k^k - b + 1 is prime: this sequence (b=2),
A301521 (b=4),
A302123 (b=6).
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[n: n in [0..500] | IsPrime(2*n^n-1)]; // Vincenzo Librandi, Nov 01 2014
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Select[Range[1000], PrimeQ[2*#^# - 1] &] (* Vaclav Kotesovec, Oct 31 2014 *)
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for(n=1,2000,1;if(isprime(2*n^n-1),print(n))) \\ Ray G. Opao, Oct 23 2014
A108879
Numbers n such that (n-1)*n^n+1 is prime.
Original entry on oeis.org
2, 4, 20, 93, 100, 1536, 2835
Offset: 1
2 is in the sequence because (2-1)*2^2+1 = 1*2^2+1 = 4+1 = 5, which is prime.
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[n: n in [1..1000] |IsPrime((n-1)*n^n+1)]; // Vincenzo Librandi, Oct 23 2014
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Select[Range[1000], PrimeQ[(# - 1) #^# + 1] &] (* Vincenzo Librandi, Oct 23 2014 *)
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isok(n) = isprime((n-1)*n^n+1); \\ Michel Marcus, Oct 23 2014
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from sympy import isprime
def afind(limit, startk=0):
for k in range(startk, limit+1):
if isprime((k-1)*k**k + 1):
print(k, end=", ")
afind(200) # Michael S. Branicky, Jan 01 2022
A353122
Numbers k such that k^k*(k+1) + 1 is prime.
Original entry on oeis.org
0, 1, 2, 3, 6, 9, 186, 198, 8390
Offset: 1
9 is in the sequence because 9^9*(9+1) + 1 = 3874204891, which is prime.
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[n: n in [0..200] | IsPrime(n^n*(n+1) + 1)];
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Join[{0}, Select[Range[200], PrimeQ[#^#*(# + 1) + 1] &]] (* Amiram Eldar, Apr 25 2022 *)
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isok(k) = ispseudoprime(k^k*(k+1) + 1); \\ Michel Marcus, May 16 2022
Showing 1-3 of 3 results.
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