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%I #19 Apr 04 2024 10:37:23
%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 lim_{n->oo} 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.....
%F a(n) = A055496(m) when a(n+1) > a(n) + 1. - _Bill McEachen_, Mar 24 2024
%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, A055496.
%K nonn
%O 1,2
%A _Benoit Cloitre_, Mar 08 2003
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