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

2, 13, 23, 13, 89, 19, 7, 47, 67, 13, 17, 157, 17, 313, 107, 409, 151, 773, 149, 409, 109, 13, 29, 211, 7, 19, 149, 431, 859, 43, 109, 167, 277, 13, 2293, 173, 907, 107, 1087, 617, 449, 1013, 73, 1249, 743, 109, 233, 499, 191, 479

Offset: 1

Author

Amarnath Murthy, Dec 07 2003

Keywords

• base
• nonn

Comments

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.

Examples

			a(5) = 89, as floor((10^5)/89) = 1123 is the largest such prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1800

Crossrefs

Cf. A090517, A090518, A090520.

Programs

Maple

f:= proc(n) local t,p;
t:= 10^n;
p:= 1;
while p < t/2 do
  p:= nextprime(p);
  if isprime(floor(t/p)) then return p fi
od;
0
end proc:
map(f, [$1..50]); # Robert Israel, Jul 30 2023

Mathematica

<Ryan Propper, Jun 19 2005 *)

Extensions

Corrected and extended by Ryan Propper, Jun 19 2005