A248595 - OEIS

%I #15 Oct 27 2014 08:24:51

%S 5,7,11,23,23,41,53,59,47,59,157,113,83,131,239,107,179,307,337,359,

%T 367,239,167,179,293,509,311,751,547,227,383,263,1511,419,449,757,787,

%U 491,503,347,359,907,383,967,593,599,1481,1117,683,1607,467,479,1693

%N Smallest prime number Q such that there is a prime number R such that floor(Q/R)=prime(n).

%H Pierre CAMI, <a href="/A248595/b248595.txt">Table of n, a(n) for n = 1..10000</a>

%e floor(3/2)=1 not prime, floor(5/2)=2=prime(1) so a(1)=5.

%e floor(7/2)=3=prime(2), so a(2)=7.

%e floor(11/2)=5=prime(3), so a(3)=11.

%e floor(13/2)=6 and floor(17/2)=8 not prime, floor(23/3)=7=prime(4), so a(4)=23.

%e floor(23/2)=11=prime(5) so a(5)=23.

%t a[n_] := For[p = Prime[n]; r = 2, True, r = NextPrime[r], For[q = NextPrime[r*p, -1], q <= (p + 1) r, q = NextPrime[q], If[Floor[q/r] == p, Return[q]]]]; Array[a, 100] (* _Jean-François Alcover_, Oct 25 2014 *)

%o ( Excel & Visual Basic, the file pre.txt with the first 1000000 prime numbers )

%o    Dim p(10000), q(1000000)

%o    Open "pre.txt" For Input As #1

%o    For i = 1 To 10000: Input #1, x: p(i) = x: q(i) = x: Next i

%o    For i = 10001 To 1000000: Input #1, x: q(i) = x: Next i

%o    o = 3

%o    For l = 1 To 10000

%o    x = p(l)

%o    For i = 1 To 10000

%o    a = p(i)

%o    For j = o To 1000000

%o    b = q(j)

%o    c = Int(b / a)

%o    If c < x Then GoTo 5

%o    If c = x Then Cells(l, 1) = x: Cells(l, 2) = b: Cells(l, 3)= a: Cells(l, 4).Select: GoTo 20

%o    GoTo 10

%o 5  Next j

%o 10 Next i

%o 20 If i = 1 Then o = j

%o    Next l

%o End Sub

%Y Cf. A248596.

%K nonn

%O 1,1

%A _Pierre CAMI_, Oct 09 2014