A350035 Number of steps to reach 1 under repeated applications of the A350034 map, or -1 if 1 is never reached.

0, 1, 1, 2, 11, 1, 3, 3, 2, 12, 7, 2, 9, 4, 12, 4, 6, 2, 6, 13, 4, 8, 16, 3, 6, 10, 3, 5, 13, 12, 12, 5, 8, 7, 12, 2, 14, 7, 10, 14, 9, 4, 4, 9, 13, 17, 21, 4, 11, 7, 7, 11, 19, 3, 19, 6, 7, 14, 18, 13, 9, 13, 5, 6, 13, 8, 8, 8, 17, 13, 20, 3, 11, 15, 7, 8, 15, 10, 10, 15, 4, 10, 15, 5, 22, 5

Offset: 1

Author

José María Grau Ribas, Jan 19 2022

Keywords

• nonn

Examples

			5 -> 26 -> 13 -> 66 -> 11 -> 56 -> 28 -> 14 -> 7 -> 36 -> 6 -> 1. Thus a(5) = 11.
		

Links

• Winston de Greef, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A350034, A006370, A089128, A006577, A133420.

Programs

Maple

a:= proc(n) option remember; `if`(n=1, 0, 1+
      a((g-> `if`(g>1, n/g, 5*n+1))(igcd(n, 6))))
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jan 19 2022

Mathematica

f[n_]:=If[GCD[n,6]>1,n/GCD[n,6],5*n+1];Table[f[n],{n,0,100}];
S[n_]:=S[n]=Which[n==1,0,f[n]==1,1,True,1+S[f[n]]];
Table[S[n],{n,1,86}]

PARI

A350034(n) = my(g = gcd(n, 6)); if (g>1, n/g, 5*n+1);
a(n)=my(r=0); while(n != 1, n = A350034(n); r+=1); r \\ Winston de Greef, Oct 02 2023