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.

4, 446, 444, 445, 448, 443, 236, 444, 441, 508, 8, 442, 511, 235, 506, 443, 514, 440, 509, 507, 233, 934, 445, 441, 512, 512, 438, 234, 937, 505, 889, 442, 515, 480, 241, 439, 239, 508, 510, 506, 892, 232, 10, 933, 503, 427, 444, 440, 461, 457, 478, 420, 509

Offset: 0

Author

Pierre CAMI, Mar 07 2018

Keywords

• nonn

Comments

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.

Examples

			For n=1 after 135 tripling(+1), 47 doubling(+1) and 263 halfing x(446)=1, so a(1)=446.
		

Crossrefs

Cf. A006577, A294748, A297307, A300286.

Programs

PARI

f(x) = if (x % 2, if (isprime(x), 2*x+1, 3*x+1), x/2);
a(n) = {x = f(2*n+1); nb = 2; while (! ((x == 1) || (x == 1163)), x = f(x); nb++); nb;} \\ Michel Marcus, Mar 07 2018