A132198 -id:A132198 - cp's OEIS frontend

A132358 a(n) = greatest prime <= 2^(2^n).

2, 3, 13, 251, 65521, 4294967291, 18446744073709551557, 340282366920938463463374607431768211297, 115792089237316195423570985008687907853269984665640564039457584007913129639747

Offset: 0

Leroy Quet, Nov 08 2007

nonn

Cf. A132198.

a={}; For[n=0, n<10, n++, b=2^(2^n); While[ !PrimeQ[b], b=b-1]; AppendTo[a, b]]; a (* Stefan Steinerberger, Nov 12 2007 *)
If[PrimeQ[#],#,NextPrime[#,-1]]&/@(2^(2^Range[0,10])) (* Harvey P. Dale, Jul 01 2020 *)

More terms from Stefan Steinerberger, Nov 12 2007

A269834 Primes p of the form 2^k + 9*(-1)^k - 8.

Original entry on oeis.org

2, 5, 17, 257, 65537

Offset: 1

Jaroslav Krizek, Mar 06 2016

nonn

Union of number 2 and Fermat primes > 3 from A019434; for odd k, the numbers 2^k - 17 are divisible by 3.
Also primes p of the form 2^k + 12*(-1)^k - 11 for k >= 0 because for odd k, the numbers 2^k - 23 are divisible by 3.
Also primes p of the form 2^k + 1/2*(q + 1)*(-1)^k - 1/2*(q - 1) for k >= 0 where q = prime of the form 3m - 1 > 29 from A003627 because for odd k, the numbers 2^k - q are divisible by 3.
Corresponding values of k:  0, 2, 4, 8, 16, ...

Sequence is different from A132198 and A111635.

Cf. A003627, A019434.

[2^n + 9*(-1)^n - 8: n in [0..1000] | IsPrime(2^n + 9*(-1)^n - 8)];

cp's OEIS Frontend

A132358 a(n) = greatest prime <= 2^(2^n).

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