A229627 a(n) is the smallest prime q such that 2*q^k - 1 is prime for k = 1, 2, ..., n.

2, 2, 3, 92581, 385939, 464938699, 24137752519, 1095265755949

Offset

1,1

Comments

The prime number 2 in the definition is used because 2 is the only prime p such that p*q^k - 1 can be prime for more than one prime q.

a(9) > 3*10^13. - Tyler Busby, Jan 14 2023

Links

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

Mathematica

a[1]=2; a[n_]:=a[n]=(For[m=PrimePi[a[n-1]], Union[Table[PrimeQ[2 Prime[m]^k-1], {k, n}]]!={True}, m++]; Prime[m])]

Prog

(PARI) a(n)=forprime(m=2, , for(k=1, n, if(!ispseudoprime(2*m^k-1), next(2))); return(m)) \\ Charles R Greathouse IV, Oct 01 2013

Crossrefs

Cf. A005382, A106483, A177104, A182785, A309855, A229626.

Sequence in context: A359354 A006560 A088251 * A140839 A320299 A357969

Adjacent sequences: A229624 A229625 A229626 * A229628 A229629 A229630

Keyword

nonn,more

Author

Farideh Firoozbakht, Sep 27 2013

Extensions

a(7) from Giovanni Resta, Oct 01 2013

a(8) from Tyler Busby, Jan 06 2023

Status

approved