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a(n) is the smallest m such that 2*m^k-1 is prime for k = 1, 2, ..., n.
3

%I #19 Jan 06 2023 22:27:03

%S 2,2,3,6,6,11256895,15682744,45779314036,687860415949

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

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

%o (PARI) a(n)=my(m=2); while(1,for(k=1, n, if(!ispseudoprime(2*m^k-1), m++; next(2))); return(m)) \\ _Charles R Greathouse IV_, Oct 01 2013

%Y Cf. A229627.

%K nonn,more

%O 1,1

%A _Farideh Firoozbakht_, Sep 27 2013

%E a(8) from _Giovanni Resta_, Oct 01 2013

%E a(9) from _Tyler Busby_, Jan 06 2023