cp's OEIS Frontend

A300507 Define the set of generalized Syracuse sequences starting with a positive odd integer 2*n+1=x(1) then if x(i) is odd and prime set x(i+1)=2*x(i)+1, if x(i) is odd not prime set x(i+1)=3*x(i)+1 and if x(i) is even then set x(i+1)=x(i)/2. a(n) is the index i when x(i) reaches 1 or 1163.

%I A300507 #11 Apr 17 2018 00:11:33
%S A300507 4,446,444,445,448,443,236,444,441,508,8,442,511,235,506,443,514,440,
%T A300507 509,507,233,934,445,441,512,512,438,234,937,505,889,442,515,480,241,
%U A300507 439,239,508,510,506,892,232,10,933,503,427,444,440,461,457,478,420,509
%N A300507 Define the set of generalized Syracuse sequences starting with a positive odd integer 2*n+1=x(1) then if x(i) is odd and prime set x(i+1)=2*x(i)+1, if x(i) is odd not prime set x(i+1)=3*x(i)+1 and if x(i) is even then set x(i+1)=x(i)/2. a(n) is the index i when x(i) reaches 1 or 1163.
%C A300507 For n<40 the sequences reach 1, for n=40 the sequence reaches 1163 for x(889) and recover 1163 for x(889+931) a cycle of 961 values.
%e A300507 For n=1 after 135 tripling(+1), 47 doubling(+1) and 263 halfing x(446)=1, so a(1)=446.
%o A300507 (PARI) f(x) = if (x % 2, if (isprime(x), 2*x+1, 3*x+1), x/2);
%o A300507 a(n) = {x = f(2*n+1); nb = 2; while (! ((x == 1) || (x == 1163)), x = f(x); nb++); nb;} \\ _Michel Marcus_, Mar 07 2018
%Y A300507 Cf. A006577, A294748, A297307, A300286.
%K A300507 nonn
%O A300507 0,1
%A A300507 _Pierre CAMI_, Mar 07 2018