A277343 a(1) is 4. a(n) is the least semiprime q (A001358) greater than p = a(n-1), such that p/q is a new minimum.

4, 6, 10, 21, 46, 106, 247, 579, 1363, 3214, 7586, 17915, 42311, 99931, 236023, 557455, 1316638, 3109733, 7344803, 17347513, 40972678, 96772393, 228564417, 539840885, 1275037411, 3011480697, 7112745019, 16799424206, 39678162637, 93714913738, 221343037931, 522784885426, 1234753254431

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

Cf. A001358, A265418.

Sequence in context: A320124 A185913 A243119 * A077065 A131867 A252656

Adjacent sequences: A277340 A277341 A277342 * A277344 A277345 A277346

Keyword

nonn

Author

Robert G. Wilson v, Oct 09 2016

Status

approved