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5, 11, 83, 769, 3571, 52631, 1428571, 3703703, 83333333, 769230769, 5882352941, 13513513513, 588235294117, 7142857142857, 12195121951219, 151515151515151, 2777777777777777, 22727272727272727, 1111111111111111111
COMMENTS
Conjecture: No term is zero.
PROG
(PARI) A090518(n)={ local(k, tenn) ; k=1 ; tenn=10^n ; while(1, if( isprime(floor(tenn/k)), return(floor(tenn/k)) ) ; k++ ; ) ; } { for(n=1, 40, print1( A090518(n), ", ") ; ) } - R. J. Mathar, Nov 19 2006
Smallest prime p such that floor((10^n)/p) is prime, or 0 if no such number exists.
+10
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
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.
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:
MATHEMATICA
<<NumberTheory`; Do[k = 2; While[ !PrimeQ[Floor[10^n / k]], k = NextPrime[k]]; Print[k], {n, 1, 50}] (* Ryan Propper, Jun 19 2005 *)
5, 7, 43, 769, 1123, 52631, 1428571, 2127659, 14925373, 769230769, 5882352941, 6369426751, 588235294117, 319488817891, 9345794392523, 24449877750611, 662251655629139, 1293661060802069, 67114093959731543, 244498777506112469
COMMENTS
Conjecture: No term is zero.
PROG
(PARI) A090520(n)={ local(p, tenn) ; p=2 ; tenn=10^n ; while(tenn/p>=2, if( isprime(floor(tenn/p)), return(floor(tenn/p)) ) ; p=nextprime(p+1) ; ) ; return(0) ; } { for(n=1, 40, print1( A090520(n), ", ") ; ) } - R. J. Mathar, Nov 19 2006
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