OFFSET
1,1
COMMENTS
Inspired by and analogous to A265418.
p/q -> 0.423392190744304142156851442297311481582158896664...
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..200
EXAMPLE
4/6 is 0.666... is a new low or minimum;
6/9 is 0.666... is not a new minimum, but;
6/10 is 0.600... is a new minimum;
10/21 is 0.476... is a new minimum;
21/46 is 0.456... is a new minimum;
... 522784885426/1234753254431 is 0.423... is a new minimum; etc.
MATHEMATICA
NextSemiPrime[n_, k_: 1] := Block[{c = 0, sgn = Sign[k]}, sp = n + sgn; While[c < Abs[k], While[PrimeOmega[sp] != 2, If[sgn < 0, sp--, sp++]]; If[sgn < 0, sp--, sp++]; c++]; sp + If[sgn < 0, 1, -1]];
p = 4; q = 6; mx = 1; lst = {}; While[q < 10^15, r = p/q; If[r < mx, mx = r; AppendTo[lst, p]; p = q]; q = NextSemiPrime[Floor[q/r]]]; lst (* or *)
f[lst_List] := Block[{p = lst[[-2]], q = lst[[-1]]}, Append[lst, NextSemiPrime[ Floor[q^2/p]]]]; lst = {4, 6}; lst = Nest[f, lst, 30]
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Oct 09 2016
STATUS
approved