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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 (list; graph; refs; listen; history; text; internal format)
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^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 *)

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

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Last modified April 2 19:05 EDT 2020. Contains 333190 sequences. (Running on oeis4.)