cp's OEIS Frontend

A090519 Smallest prime p such that floor((10^n)/p) is prime, or 0 if no such number exists.

%I A090519 #13 Jul 31 2023 10:08:08
%S A090519 2,13,23,13,89,19,7,47,67,13,17,157,17,313,107,409,151,773,149,409,
%T A090519 109,13,29,211,7,19,149,431,859,43,109,167,277,13,2293,173,907,107,
%U A090519 1087,617,449,1013,73,1249,743,109,233,499,191,479
%N A090519 Smallest prime p such that floor((10^n)/p) is prime, or 0 if no such number exists.
%C A090519 Conjecture: No term is zero. Subsidiary Sequence: Number of primes in floor((10^n)/p), p is a prime. a(1) = 3, the primes are 10/2, floor(10/3) and 10/5.
%H A090519 Robert Israel, <a href="/A090519/b090519.txt">Table of n, a(n) for n = 1..1800</a>
%e A090519 a(5) = 89, as floor((10^5)/89) = 1123 is the largest such prime.
%p A090519 f:= proc(n) local t,p;
%p A090519 t:= 10^n;
%p A090519 p:= 1;
%p A090519 while p < t/2 do
%p A090519   p:= nextprime(p);
%p A090519   if isprime(floor(t/p)) then return p fi
%p A090519 od;
%p A090519 0
%p A090519 end proc:
%p A090519 map(f, [$1..50]); # _Robert Israel_, Jul 30 2023
%t A090519 <<NumberTheory`; Do[k = 2; While[ !PrimeQ[Floor[10^n / k]], k = NextPrime[k]]; Print[k], {n, 1, 50}] (* _Ryan Propper_, Jun 19 2005 *)
%Y A090519 Cf. A090517, A090518, A090520.
%K A090519 base,nonn
%O A090519 1,1
%A A090519 _Amarnath Murthy_, Dec 07 2003
%E A090519 Corrected and extended by _Ryan Propper_, Jun 19 2005