A187602
Primes of the form (k+1)^(k-1) + k.
Original entry on oeis.org
2, 5, 19, 1301, 262151, 4782977
Offset: 1
1301 is in the sequence since it is prime and, using k = 5, (k+1)^(k-1) + k = 6^4 + 5 = 1296 + 5 = 1301.
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Do[p=(n+1)^(n-1)+n; If[PrimeQ[p], Print[p]], {n, 250}]
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lista(nn) = for(k=1, nn, if(ispseudoprime(q=(k+1)^(k-1)+k), print1(q, ", "))); \\ Jinyuan Wang, Mar 01 2020
A240532
Numbers k such that (k+1)^(k-1) - k is prime.
Original entry on oeis.org
3, 5, 8, 17, 30, 66, 86, 100, 122, 160, 2282, 6508
Offset: 1
3 is in the sequence since (3+1)^(3-1) - 3 = 4^2 - 3 = 13 is prime.
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[n: n in [1..500] | IsPrime((n+1)^(n-1)-n)];
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Select[Range[0, 500], PrimeQ[(# + 1)^(# - 1) - #] &]
n=0;Monitor[Parallelize[While[True,If[PrimeQ[(n+1)^(n-1)-n],Print[n]];n++];n],n] (* J.W.L. (Jan) Eerland, Dec 23 2021 *)
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is(n)=isprime((n+1)^(n-1)-n) \\ Charles R Greathouse IV, Jun 13 2017
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from sympy import isprime
def afind(limit, startk=1):
for k in range(startk, limit+1):
if isprime((k+1)**(k-1) - k): print(k, end=", ")
afind(200) # Michael S. Branicky, Aug 17 2021
A382370
Numbers k such that (k - 1)^(k + 1) - k is prime.
Original entry on oeis.org
3, 4, 5, 7, 10, 11, 21, 46, 59, 839, 21920
Offset: 1
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[k: k in [2..500] | IsPrime((k-1)^(k+1)-k)];
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Select[Range[1000], PrimeQ[(#-1)^(#+1)-#] &] (* Stefano Spezia, Mar 30 2025 *)
Showing 1-3 of 3 results.
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