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

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

Offset

1,1

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.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..19

Wikipedia, Woodall number

Example

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.

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 *)

Crossrefs

Cf. A003261, A072669.

Sequence in context: A001136 A256172 A142939 * A036335 A075931 A142440

Adjacent sequences: A229015 A229016 A229017 * A229019 A229020 A229021

Keyword

nonn

Author

K. D. Bajpai, Sep 11 2013

Status

approved