A274472 -id:A274472 - cp's OEIS frontend

A322973 Lexicographically earliest such sequence a that a(i) = a(j) => f(i) = f(j) for all i, j, where f(1) = 0, f(n) = -1 if n is an odd prime, and f(n) = A006370(n) for all other numbers.

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 11, 12, 3, 13, 3, 14, 15, 16, 3, 17, 18, 19, 20, 21, 3, 22, 3, 23, 24, 25, 26, 27, 3, 28, 29, 30, 3, 31, 3, 32, 33, 34, 3, 35, 36, 37, 38, 39, 3, 40, 41, 7, 42, 43, 3, 44, 3, 45, 46, 47, 48, 49, 3, 50, 51, 52, 3, 53, 3, 54, 55, 56, 57, 58, 3, 59, 60, 61, 3, 62, 63, 64, 65, 66, 3, 67, 68, 11, 69, 70, 71, 72, 3, 73, 74, 75, 3, 76, 3

Offset: 1

Antti Karttunen, Jan 05 2019

nonn

For all i, j: a(i) = a(j) => A274472(i) = A274472(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to 3x+1 (or Collatz) problem

Cf. A006370, A274472, A305801.

See the crossrefs section in A322809 for a list of similarly constructed filter sequences.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A006370(n) = if(n%2, 3*n+1, n/2);
A322973aux(n) = if(1==n,0,if((n>2)&&isprime(n),-1,A006370(n)));
v322973 = rgs_transform(vector(up_to,n,A322973aux(n)));
A322973(n) = v322973[n];

A280929 Number of steps required to reach the first prime when starting from n in the Collatz (or '3x+1') problem.

Original entry on oeis.org

2, 3, 2, 1, 4, 1, 2, 2, 3, 1, 2, 2, 4, 1, 2, 3, 3, 4, 2, 2, 6, 1, 4, 3, 3, 1, 2, 2, 4, 3, 2, 4, 6, 1, 2, 5, 5, 1, 2, 3, 3, 7, 8, 2, 4, 1, 2, 4, 3, 4, 6, 2, 6, 3, 2, 3, 3, 1, 2, 4, 4, 1, 17, 5, 6, 7, 2, 2, 5, 3, 2, 6, 5, 1, 2, 2, 4, 3, 4, 4, 3, 1, 6, 8, 8, 1, 2, 3, 3, 5, 2, 2, 6, 1, 15, 5, 3, 4, 2, 5

Offset: 1

Dmitry Kamenetsky, Jan 11 2017

nonn

If n=p*2^k, where k>0 and p is some prime then a(n)=k.
If n is odd then a(n)=a(3n+1)+1.
If n is even then a(n)=1 or a(n)=a(n/2)+1.
If n is composite then a(n)=A274472(n).

			The Collatz iteration for 33 is 100, 50, 25, 76, 38, 19, 58, 29, ... 1. The first prime (19) is reached after 6 steps, so a(33)=6.

Dmitry Kamenetsky, Table of n, a(n) for n = 1..10000

Cf. A006577, A274472.

cp's OEIS Frontend

A322973 Lexicographically earliest such sequence a that a(i) = a(j) => f(i) = f(j) for all i, j, where f(1) = 0, f(n) = -1 if n is an odd prime, and f(n) = A006370(n) for all other numbers.

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