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A229630 a(n) is the smallest semiprime m such that 2*m^k-1 is prime for k = 1, 2, ..., n. 0
4, 4, 4, 6, 6, 118909855, 5740959589, 79235997091 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..8.

EXAMPLE

a(5)=6 because 2*6^k-1 is prime for k=1,2,3,4,5 and 6 is the smallest semiprime with this property. Also 6 is the smallest such number.

MATHEMATICA

a[n_]:=(For[m=1, !(2<Length[Divisors[m]]<5&&Union[Table[PrimeQ[2m^k-1], {k, n}]]=={True}), m++]; m); Do[Print[a[n]], {n, 7}]

PROG

(PARI) \\ Code to find a(8), can be modified to find other terms easily

issemi(n)=bigomega(n)==2

is8(m)=for(i=2, 8, if(!ispseudoprime(2*m^i-1), return(0))); 1

forprime(p=2, 1e12, m=(p+1)/2; if(issemi(m)&&is8(m), return(m))) \\ Charles R Greathouse IV, Oct 17 2013

CROSSREFS

Cf. A229626, A229627, A229902.

Sequence in context: A097918 A256416 A256417 * A141466 A171743 A295641

Adjacent sequences:  A229627 A229628 A229629 * A229631 A229632 A229633

KEYWORD

nonn,more

AUTHOR

Farideh Firoozbakht, Oct 14 2013

EXTENSIONS

a(8) from Charles R Greathouse IV, Oct 17 2013

STATUS

approved

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Last modified February 22 08:35 EST 2020. Contains 332133 sequences. (Running on oeis4.)