A294748 Define one of the generalized Syracuse sequences starting with a positive odd integer 2*k+1=x(1), then if x(i) is an odd prime set x(i+1)=2*x(i)+1, if x(i) is odd not prime set x(i+1)=3*x(i)+1, if x(i) is even then set x(i+1)=x(i)/2. This sequence gives the positive odd integers 2*k+1=x(1) for sequences reaching x(i)=1.

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 63, 65, 67, 69, 71, 73, 75, 77, 79, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 125, 127, 129, 131, 133, 135, 137, 141, 143, 145

Offset: 1

Author

Pierre CAMI, Feb 18 2018

Keywords

• nonn

Comments

The sequence of positive odd integers not in this sequence begins {61, 81, 123, 139, ...}. When x(1) is any of these, the sequence x(i) enters a cycle of 931 values x(i) = x(i+931)=1163.

Links

• Pierre CAMI, PFGW Script

Crossrefs

Cf. A006577, A297307, A300286.

Programs

PARI

f(n) = if (n % 2, if (isprime(n), 2*n+1, 3*n+1), n/2);
isok(n) = {if (n%2, while (1, n = f(n); if (n==1, return (1)); if (n==1163, return (0));););} \\ Michel Marcus, Mar 28 2018