A050918 Woodall primes: primes of form k*2^k-1.

7, 23, 383, 32212254719, 2833419889721787128217599, 195845982777569926302400511, 4776913109852041418248056622882488319, 1307960347852357218937346147315859062783, 225251798594466661409915431774713195745814267044878909733007331390393510002687

Offset: 1

Author

N. J. A. Sloane, Dec 30 1999

Keywords

• nonn
• easy
• nice

Links

• M. F. Hasler, Table of n, a(n) for n = 1..15 (all terms < 10^999).
• Ray Ballinger, Woodall Primes: Definition and Status.
• C. K. Caldwell, Woodall Numbers.
• Brady Haran and Matt Parker, 383 is cool, Numberphile video, 2017.
• Eric Weisstein's World of Mathematics, Woodall Number.

Crossrefs

Cf. A002234, A003261.

Programs

Mathematica

Select[Table[n 2^n - 1, {n, 300}], PrimeQ] (* Harvey P. Dale, Jul 12 2012 *)

PARI

for(n=2,999,ispseudoprime(p=n*2^n-1)&&print1(p",")) \\ M. F. Hasler, May 10 2017

Python

from sympy import isprime
def auptok(limit):
    return list(filter(isprime, (k*2**k-1 for k in range(1, limit+1))))
print(auptok(1000)) # Michael S. Branicky, Jul 23 2021

Formula

a(n) = A002234(n)*2^A002234(n) - 1. - M. F. Hasler, May 10 2017