A083005 - OEIS

%I #13 Jul 02 2021 13:08:42

%S 1,2,5,11,23,47,95,96,97,195,196,197,395,396,397,795,796,797,1595,

%T 1596,1597,3195,3196,3197,3198,3199,3200,3201,3202,3203,6407,6408,

%U 6409,6410,6411,6412,6413,6414,6415,6416,6417,6418,6419,6420,6421,12843,12844

%N a(1)=1, a(n)=2a(n-1)+1 if a(n-1) is prime, a(n)=a(n-1)+1 otherwise.

%C Primes in this sequence are A055496.- _Robert Israel_, May 23 2017

%H Robert Israel, <a href="/A083005/b083005.txt">Table of n, a(n) for n = 1..10197</a>

%F Conjecture : limit n ->oo log(a(n))/sqrt(n)=c= 1.3....

%p P[0]:= 0:

%p for n from 2 to 20 do P[n]:= nextprime(2*P[n-1]) od:

%p seq($2*P[i]+1..P[i+1],i=0..19); # _Robert Israel_, May 23 2017

%t NestList[If[PrimeQ[#],2#+1,#+1]&,1,50] (* _Harvey P. Dale_, Jul 02 2021 *)

%Y Cf. A055496.

%K nonn

%O 1,2

%A _Benoit Cloitre_, May 31 2003

%E Offset corrected by _Robert Israel_, May 23 2017