A248595 Smallest prime number Q such that there is a prime number R such that floor(Q/R)=prime(n).

5, 7, 11, 23, 23, 41, 53, 59, 47, 59, 157, 113, 83, 131, 239, 107, 179, 307, 337, 359, 367, 239, 167, 179, 293, 509, 311, 751, 547, 227, 383, 263, 1511, 419, 449, 757, 787, 491, 503, 347, 359, 907, 383, 967, 593, 599, 1481, 1117, 683, 1607, 467, 479, 1693

Offset

1,1

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000

Example

floor(3/2)=1 not prime, floor(5/2)=2=prime(1) so a(1)=5.
floor(7/2)=3=prime(2), so a(2)=7.
floor(11/2)=5=prime(3), so a(3)=11.
floor(13/2)=6 and floor(17/2)=8 not prime, floor(23/3)=7=prime(4), so a(4)=23.
floor(23/2)=11=prime(5) so a(5)=23.

Mathematica

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 *)

Prog

( Excel & Visual Basic, the file pre.txt with the first 1000000 prime numbers )
   Dim p(10000), q(1000000)
   Open "pre.txt" For Input As #1
   For i = 1 To 10000: Input #1, x: p(i) = x: q(i) = x: Next i
   For i = 10001 To 1000000: Input #1, x: q(i) = x: Next i
   o = 3
   For l = 1 To 10000
   x = p(l)
   For i = 1 To 10000
   a = p(i)
   For j = o To 1000000
   b = q(j)
   c = Int(b / a)
   If c < x Then GoTo 5
   If c = x Then Cells(l, 1) = x: Cells(l, 2) = b: Cells(l, 3)= a: Cells(l, 4).Select: GoTo 20
   GoTo 10
5  Next j
10 Next i
20 If i = 1 Then o = j
   Next l
End Sub

Crossrefs

Cf. A248596.

Sequence in context: A057733 A318078 A174332 * A266233 A124111 A151715

Adjacent sequences: A248592 A248593 A248594 * A248596 A248597 A248598

Keyword

nonn

Author

Pierre CAMI, Oct 09 2014

Status

approved