This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A080735 #19 Apr 04 2024 10:37:23
%S A080735 1,2,4,5,10,11,22,23,46,47,94,95,96,97,194,195,196,197,394,395,396,
%T A080735 397,794,795,796,797,1594,1595,1596,1597,3194,3195,3196,3197,3198,
%U A080735 3199,3200,3201,3202,3203,6406,6407,6408,6409,6410,6411,6412,6413,6414,6415,6416
%N A080735 a(1)=1, then a(n)=2*a(n-1) if a(n-1) is prime, a(n)=a(n-1)+1 otherwise.
%C A080735 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 A080735 Harvey P. Dale, <a href="/A080735/b080735.txt">Table of n, a(n) for n = 1..1000</a>
%F A080735 It seems that log(a(n))/sqrt(n) -> C, a constant around 1.3.....
%F A080735 a(n) = A055496(m) when a(n+1) > a(n) + 1. - _Bill McEachen_, Mar 24 2024
%t A080735 NestList[If[PrimeQ[#],2#,#+1]&,1,50] (* _Harvey P. Dale_, Aug 26 2013 *)
%o A080735 (PARI) u=1; for(n=2,100,v=if(isprime(u),u+1,2*u); u=v; print1(v,","))
%Y A080735 Cf. A163962, A055496.
%K A080735 nonn
%O A080735 1,2
%A A080735 _Benoit Cloitre_, Mar 08 2003