A230168 Primes of the form 45*2^n - 1.

89, 179, 359, 719, 1439, 2879, 11519, 23039, 737279, 1474559, 2949119, 188743679, 12079595519, 24159191039, 3092376453119, 6184752906239, 810647932926689279, 25940733853654056959, 1740853180245066011576893439, 445658414142736898963684720639

Offset: 1

Author

K. D. Bajpai, Oct 11 2013

Keywords

• nonn

Comments

Conjecture: each term in the sequence ends with digit 9.

The expression k*2^n - 1 with k = 45 yields more primes than any other value of k = 1 to 100 and n = 1000.

The term a(44) has 939 digits; a(45) has 1026 digits; a(50) has 2706 digits. - Bajpai

Each term is congruent to 89 mod 90 and therefore each term in the sequence ends in 9. This is a very simple consequence of the definition. - Alonso del Arte, Oct 11 2013

Examples

			a(4) = 719: 45*2^4 - 1 = 719, which is prime.
a(9) = 737279: 45*2^14 - 1 = 737279, which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..44

Crossrefs

Cf. A050522.

Programs

Maple

KD:= proc() local a; a:=45*2^n-1; if isprime(a) then return (a) : fi; end: seq(KD(),n=1..1000);

Mathematica

Select[2^Range[100]45 - 1, PrimeQ] (* Alonso del Arte, Oct 11 2013 *)