A328314 Lexicographically earliest infinite sequence such that a(i) = a(j) => A025586(i) = A025586(j) for all i, j.

1, 2, 3, 4, 3, 3, 5, 6, 5, 3, 5, 3, 7, 5, 8, 3, 5, 5, 9, 10, 11, 5, 8, 12, 9, 7, 13, 5, 9, 8, 13, 14, 15, 5, 8, 5, 16, 9, 17, 7, 13, 11, 18, 5, 19, 8, 13, 20, 21, 9, 22, 5, 8, 13, 13, 23, 18, 9, 17, 8, 24, 13, 13, 11, 18, 15, 17, 25, 26, 8, 13, 27, 13, 16, 28, 9, 22, 17, 29, 30, 31, 13, 13, 32, 33, 18, 34, 9, 17, 19, 13, 8, 35

Offset: 1

Author

Antti Karttunen, Oct 14 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of A025586, the largest value in '3x+1' trajectory of n.

Links

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

Crossrefs

Cf. A025586.

Cf. also A322973.

Programs

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; };
A025586(n) = { my(r=n); while(n>2, if(n%2, n=3*n+1; if(n>r, r=n), n/=2)); (r); }; \\ From A025586
v328314 = rgs_transform(vector(up_to, n, A025586(n)));
A328314(n) = v328314[n];