A216148
Primes of the form 2*k^k + 1 = A216147(k).
Original entry on oeis.org
3, 17832200896513, 78692816150593075150849
Offset: 1
A subsequence of
A133663, with b=a and c=1.
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Select[Table[2n^n+1,{n,20}],PrimeQ] (* Harvey P. Dale, Mar 27 2016 *)
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for(n=1,999, ispseudoprime(p=n^n*2+1) & print1(p","))
A174711
Composites of the form 2*n^n + 1 = A216147(n).
Original entry on oeis.org
9, 55, 513, 6251, 93313, 1647087, 33554433, 774840979, 20000000001, 570623341223, 605750213184507, 22224013651116033, 875787780761718751, 36893488147419103233, 1654480523772673528355, 3956839311320627178247959
Offset: 1
a(2) = 9 = 3^2, a(3) = 55 = 5*11, a(4) = 513 = 3 ^ 3 * 19.
- T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976.
- J. M. De Koninck, A. Mercier, 1001 problemes en theorie classique des nombres, Ellipses 2004, p. 52.
- G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 2.
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with(numtheory):for n from 0 to 50 do: x:=2*n^n + 1 : if type(x,prime)=false then print (x):else fi:od:
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Select[Table[2n^n+1,{n,20}],CompositeQ] (* Harvey P. Dale, Jun 21 2015 *)
A110932
Numbers k such that 2*k^k + 1 is prime.
Original entry on oeis.org
0, 1, 12, 18, 251, 82992
Offset: 0
A160600
Numbers k such that 3*(2k)^(2k)+1 is prime.
Original entry on oeis.org
1, 2, 3, 5, 143, 225
Offset: 1
a(1) = 1, because 2^2*3+1 = 13 is the smallest prime of this form.
a(2) = 2, because 4^4*3+1 = 769 is the next smallest prime of this form. a(3) = 3, because 6^6*3+1 = 139969 is again a prime.
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q:= k-> isprime(3*(2*k)^(2*k)+1):
select(q, [$1..225])[]; # Alois P. Heinz, Aug 04 2025
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for(i=1,9999,ispseudoprime(i^i*3+1)&print1(i/2,","))
Showing 1-4 of 4 results.
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