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A090519
Smallest prime p such that floor((10^n)/p) is prime, or 0 if no such number exists.
5
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
1,1
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.
LINKS
EXAMPLE
a(5) = 89, as floor((10^5)/89) = 1123 is the largest such prime.
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
<<NumberTheory`; Do[k = 2; While[ !PrimeQ[Floor[10^n / k]], k = NextPrime[k]]; Print[k], {n, 1, 50}] (* Ryan Propper, Jun 19 2005 *)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Dec 07 2003
EXTENSIONS
Corrected and extended by Ryan Propper, Jun 19 2005
STATUS
approved