A300286 -id:A300286 - cp's OEIS frontend

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

Pierre CAMI, Feb 18 2018

nonn

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.

Pierre CAMI, PFGW Script

Cf. A006577, A297307, A300286.

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

A300507 Define the set of generalized Syracuse sequences starting with a positive odd integer 2n+1=x(1) then if x(i) is odd and prime set x(i+1)=2x(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.

Original entry on oeis.org

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

Pierre CAMI, Mar 07 2018

nonn

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.

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

Cf. A006577, A294748, A297307, A300286.

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

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A300507 Define the set of generalized Syracuse sequences starting with a positive odd integer 2n+1=x(1) then if x(i) is odd and prime set x(i+1)=2x(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.

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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.

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A300507 Define the set of generalized Syracuse sequences starting with a positive odd integer 2n+1=x(1) then if x(i) is odd and prime set x(i+1)=2x(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.