A090520 -id:A090520 - cp's OEIS frontend

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

Amarnath Murthy, Dec 07 2003

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.

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

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

Cf. A090517, A090518, A090520.

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
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<Ryan Propper, Jun 19 2005 *)
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Corrected and extended by Ryan Propper, Jun 19 2005

A090518 Primes arising in A090517, or 0 if A090517(n) = 0.

Original entry on oeis.org

5, 11, 83, 769, 3571, 52631, 1428571, 3703703, 83333333, 769230769, 5882352941, 13513513513, 588235294117, 7142857142857, 12195121951219, 151515151515151, 2777777777777777, 22727272727272727, 1111111111111111111

Offset: 1

Amarnath Murthy, Dec 07 2003

Conjecture: No term is zero.

Cf. A090517, A090519, A090520.

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

Corrected and extended by R. J. Mathar, Nov 19 2006

A090517 Least k such that floor[(10^n)/k] is prime.

Original entry on oeis.org

2, 9, 12, 13, 28, 19, 7, 27, 12, 13, 17, 74, 17, 14, 82, 66, 36, 44, 9, 36, 21, 13, 9, 90, 7, 19, 149, 51, 321, 35, 12, 14, 140, 13, 28, 42, 34, 36, 153, 155, 133, 46, 73, 106, 162, 109, 122, 42, 62, 422, 29, 231, 38, 34, 340, 295, 151, 197, 94, 19, 17, 83, 131, 66, 36

Offset: 1

Amarnath Murthy, Dec 07 2003

			a(1) = 2 as 10/2 = 5 is a prime. a(3) = 12 as floor[1000/12] = 83 is prime.

Cf. A090518, A090519, A090520.

lkp[n_]:=Module[{k=2,c=10^n},While[!PrimeQ[Floor[c/k]],k++];k]; Array[ lkp,70] (* Harvey P. Dale, Jul 09 2018 *)

Corrected and extended by Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Jan 28 2004

Further terms from David Wasserman, Dec 20 2005

cp's OEIS Frontend

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

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A090518 Primes arising in A090517, or 0 if A090517(n) = 0.

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A090517 Least k such that floor[(10^n)/k] is prime.

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