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

3, 17832200896513, 78692816150593075150849

Offset: 1

Author

M. F. Hasler, Sep 02 2012

Keywords

• nonn
• bref
• less

Comments

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.

Links

• 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

Crossrefs

Cf. A110932.

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

Programs

Mathematica

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

PARI

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

Formula

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

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