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A080735 a(1)=1, then a(n)=2*a(n-1) if a(n-1) is prime, a(n)=a(n-1)+1 otherwise. 2


%S 1,2,4,5,10,11,22,23,46,47,94,95,96,97,194,195,196,197,394,395,396,

%T 397,794,795,796,797,1594,1595,1596,1597,3194,3195,3196,3197,3198,

%U 3199,3200,3201,3202,3203,6406,6407,6408,6409,6410,6411,6412,6413,6414,6415,6416

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

%C Conjectures: (Strong) Let x,y be 2 positive integers and define a(n) as a(1)=1, a(n)=x*a(n-1) if a(n-1) is prime, a(n)=a(n-1)+y otherwise; then limit n ->infinity log(a(n))/sqrt(n)=C(x,y) exists. (Weak) log(a(n))/sqrt(n) is bounded.

%H Harvey P. Dale, <a href="/A080735/b080735.txt">Table of n, a(n) for n = 1..1000</a>

%F It seems that log(a(n))/sqrt(n) -> C, a constant around 1.3.....

%t NestList[If[PrimeQ[#],2#,#+1]&,1,50] (* _Harvey P. Dale_, Aug 26 2013 *)

%o (PARI) u=1; for(n=2,100,v=if(isprime(u),u+1,2*u); u=v; print1(v,","))

%Y Cf. A163962.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Mar 08 2003

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Last modified January 23 00:51 EST 2018. Contains 298093 sequences.