A086661 Numbers k such that k*4^k-1 is prime.

1, 2, 3, 5, 8, 14, 23, 63, 107, 132, 428, 530, 1137, 1973, 2000, 7064, 20747, 79574, 113570, 293912, 1993191

Offset

1,2

Comments

2, 3, 5, 23, 107, 1973, 20747 is the subsequence of prime terms.

References

H. Dubner, Generalized Cullen Numbers, J. Rec. Math, 21 (No. 3, 1989).

Links

Table of n, a(n) for n=1..21.

Steven Harvey, Generalized Woodall Search

Example

2 is in the sequence because 2*4^2-1=31 is prime.
3 is in the sequence because 3*4^3-1=191 is prime.

Mathematica

Do[If[PrimeQ[n*4^n-1], Print[n]], {n, 4000}]
Select[Range[2000], PrimeQ[# 4^#-1]&] (* Harvey P. Dale, Nov 09 2024 *)

Prog

(PARI) is(n)=ispseudoprime(n*4^n-1) \\ Charles R Greathouse IV, May 22 2017

Crossrefs

Cf. A007646, A002234, A005849.

Sequence in context: A062692 A182024 A316474 * A018154 A340215 A114831

Adjacent sequences: A086658 A086659 A086660 * A086662 A086663 A086664

Keyword

nonn,more

Author

Farideh Firoozbakht, Jul 27 2003

Extensions

One more term from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Nov 23 2004

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008

Prepended first terms 1 and 2 - Pierre CAMI, Jul 21 2014

a(20)-a(21) from Harvey link by Ray Chandler, Apr 10 2016

Status

approved