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
Keywords
Examples
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.
Links
- Robert G. Wilson v, Table of n, a(n) for n = 1..200
Programs
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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]
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