

A230168


Primes of the form 45*2^n  1.


1



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

1,1


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


LINKS

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


EXAMPLE

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


MAPLE

KD:= proc() local a; a:=45*2^n1; 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 *)


CROSSREFS

Cf. A050522.
Sequence in context: A260868 A106758 A142335 * A325082 A033670 A044421
Adjacent sequences: A230165 A230166 A230167 * A230169 A230170 A230171


KEYWORD

nonn


AUTHOR

K. D. Bajpai, Oct 11 2013


STATUS

approved



