A070855 -id:A070855 - cp's OEIS frontend

A216148 Primes of the form 2*k^k + 1 = A216147(k).

3, 17832200896513, 78692816150593075150849

Offset: 1

M. F. Hasler, Sep 02 2012

The sequence should be extended through A110932, which lists the corresponding values of k: The next term, 2*251^251 + 1 = A216147(A110932(4)) ~ 4.16*10^602, is too large to include here.

M. F. Hasler, Table of n, a(n) for n = 1..4
C. Caldwell, G.L. Honaker (Eds), Prime Curios!: 78692816150593075150849.
"Jim", Topic: The Lost Proof of Fermat, on mathforum.org, Jan 31 2004

Cf. A110932.

A subsequence of A133663, with b=a and c=1.

Select[Table[2n^n+1,{n,20}],PrimeQ] (* Harvey P. Dale, Mar 27 2016 *)

for(n=1,999, ispseudoprime(p=n^n*2+1) & print1(p","))

a(2) = A216147(12) = A005109(95) = A070855(12) = A058383(89) = A133663(18).

a(3) = A216147(18) = A005109(183)= A070855(18) = A058383(177)= A133663(36).

A175763 Least k such that k*n^n + 1 is prime.

Original entry on oeis.org

1, 1, 4, 1, 12, 3, 4, 10, 10, 3, 86, 2, 40, 31, 28, 12, 8, 2, 34, 19, 28, 19, 116, 75, 4, 15, 110, 7, 8, 79, 42, 36, 14, 112, 80, 11, 30, 67, 78, 226, 170, 108, 96, 205, 272, 18, 54, 98, 42, 15, 78, 63, 362, 115, 292, 40, 170, 60, 350, 16, 366, 108, 234, 448, 128, 63, 42, 72

Offset: 1

Charles R Greathouse IV, Aug 31 2010

nonn

By Linnik's theorem, a(n) = O(n^(L*n)) for some effectively computable L.

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Cf. A070855.

lk[n_]:=Module[{c=n^n,k=1},While[!PrimeQ[k*c+1],k++];k]; Array[lk,70] (* Harvey P. Dale, Apr 10 2019 *)

a(n)=my(N=n^n,k=1);while(!isprime(k*n^n+1),k++);k

cp's OEIS Frontend

A216148 Primes of the form 2*k^k + 1 = A216147(k).

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