A258868 - OEIS

%I #16 Sep 23 2016 11:52:52

%S 1,1,2,5,26,287,356,395,544,11008,21957,32125,42450,50867,55408,

%T 206970,358276,384287,403461,735802,783831,969795,1192950,1383108

%N a(n) is the smallest integer >= a(n-1) such that prime(n)*2^a(n)-1 is a prime number.

%H K. Bonath, <a href="http://www.rieselprime.de">Riesel and Proth Prime Database</a> (2015)

%e 2*2^1-1=3 prime so a(1)=1.

%e 3*2^1-1=5 prime so a(2)=1.

%e 5*2^1-1=9 composite, 5*2^2-1=19 prime so a(3)=2.

%p A258868 := proc(n)

%p     option remember;

%p     if n = 0 then

%p         0;

%p     else

%p         for a from procname(n-1) do

%p             ithprime(n)*2^a-1 ;

%p             if isprime(%) then

%p                 return a;

%p             fi ;

%p         end do:

%p     end if;

%p end proc: # _R. J. Mathar_, Sep 23 2016

%t lst={1};Do[x=Last[lst];Label[begin];

%t If[PrimeQ[Prime[n]*2^x-1],AppendTo[lst,x],x=x+1;Goto[begin]],{n,2,9}];lst

%t (* _Ivan N. Ianakiev_, Jun 19 2015 *)

%o (PARI) first(n)=my(t,p); vector(n,i, p=prime(i); while(!ispseudoprime(p<<t-1), t++); t) \\ _Charles R Greathouse IV_, Jul 03 2015

%Y Cf. A128979.

%K nonn

%O 1,3

%A _Pierre CAMI_, Jun 13 2015