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

1,2

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to 3x+1 (or Collatz) problem

Prog

(PARI)
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];

Crossrefs

Cf. A006370, A274472, A305801.

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

Sequence in context: A319349 A353520 A361021 * A305890 A305801 A075850

Adjacent sequences: A322970 A322971 A322972 * A322974 A322975 A322976

Keyword

nonn

Author

Antti Karttunen, Jan 05 2019

Status

approved