A229018 Primes of the form (3*x + 2)*2^x - 1.

31, 223, 1279, 3276799, 14680063, 420906795007, 2357352929951743, 32326824857489154029020587706017980088319, 173918694842377447266238495093237679339055972614143

Offset: 1

Author

K. D. Bajpai, Sep 11 2013

Keywords

• nonn

Comments

Also primes of the form W(n) + W(n+1) + 1 where W(n) and W(n+1) are consecutive Woodall numbers. The n-th Woodall number = n*2^n-1.

Examples

			a(2) = 223:   for x=4: R= x*2^x-1 = 4*2^4-1 = 63 and S=  (x+1)*2^(x+1)-1 = 5*2^5-1 = 159. R+S+1 = 63+159+1 = 223 which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..19
• Wikipedia, Woodall number

Crossrefs

Cf. A003261, A072669.

Programs

Maple

KD:= proc() local a,b,d;  a:= x*2^x-1;  b:=(x+1)*2^(x+1)-1;  d:=a+b+1;  if isprime(d) then   RETURN(d): fi; end: seq(KD(),x=1..1000);

Mathematica

Select[Table[(3*x + 2)*2^x - 1, {x, 200}], PrimeQ] (* T. D. Noe, Sep 20 2013 *)