A304123 Denominators of records low values of the ratio n*3^A006667(n)/2^A006666(n).

1, 32, 2048, 8192, 2199023255552, 144115188075855872, 576460752303423488, 2305843009213693952

Offset

1,2

Links

Table of n, a(n) for n=1..8.

Example

For n=1 to 10 the ratios are 1, 1, 27/32, 1, 15/16, 27/32, 1701/2048, 1, 6561/8192, 15/16, so the low records are 1, 27/32, 1701/2048, 6561/8192, ...

Mathematica

q=1; Collatz[n_]:=NestWhileList[If[EvenQ[#], #/2, 3 #+1]&, n, #>1&]; nn=5000; t={}; n=0; While[Length[t]<nn, n++; c=Collatz[n]; ev=Length[Select[c, EvenQ]]; od=Length[c]-ev-1; If[n*3^od/2^ev<q, Print[n, " ", od, " ", ev, " ", n*3^od/2^ev]; q=n*3^od/2^ev]]

Prog

(PARI) ht(n) = my(h, t); while(n>1, if(n%2, n=3*n+1; t++, n>>=1; h++)); return([h, t]);
lista(nn) = {m = 2; for (n=1, nn, v = ht(n); newm = n*3^v[2]/2^v[1]; if (newm < m, print1(denominator(newm), ", "); m = newm)); } \\ Michel Marcus, May 06 2018

Crossrefs

Cf. A127789 (for the indices where these records occur).

Cf. A304119 (for the corresponding numerators).

Cf. A006666, A006667.

Sequence in context: A264015 A239646 A323540 * A291826 A302270 A301846

Adjacent sequences: A304120 A304121 A304122 * A304124 A304125 A304126

Keyword

nonn,frac,more

Author

Michel Lagneau, May 06 2018

Status

approved