A231755 Primes of the form (2^n-1)/3 - n.

331, 1398079, 89478457, 393530540239137101071, 1730765619511609209510165443073253, 8173309551284740577911184144801648979299941984979211421, 2142584059011987034055949456454883470029603991710390447068299

Offset: 1

Author

K. D. Bajpai, Nov 13 2013

Keywords

• nonn
• less

Comments

a(14) has 671 digits. a(15) has 2820 digits (not included in b-file).

Alternately, primes of the form Jacobsthal(n) - n, where Jacobsthal(n) is the n-th Jacobsthal number.

Examples

			a(2)= 1398079: n=22: ((2^n-(-1)^n)/3-n)= 1398079, which is prime.
a(4)= 393530540239137101071: n=70: ((2^n-(-1)^n)/3-n)= 393530540239137101071, which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..14

Crossrefs

Cf. A001045 (Jacobsthal numbers).

Cf. A107036 (indices of prime Jacobsthal numbers).

Cf. A128209 (Jacobsthal numbers+1).

Programs

Maple

KD := proc() local a; a:= (2^n -(-1)^n)/3-n; if isprime(a)then RETURN (a); fi; end: seq(KD(),n=1..1000);

PARI

for(n=8,500,if(ispseudoprime(t=2^n\/3-n),print1(t", "))) \\ Charles R Greathouse IV, Nov 13 2013

Extensions

Definition corrected by Charles R Greathouse IV, Nov 13 2013