A090520 -id:A090520

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A090519

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

(list; graph; refs; listen; history; text; internal format)

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

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

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;

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

Cf. A090517, A090518, A090520.

KEYWORD

base,nonn

AUTHOR

Amarnath Murthy, Dec 07 2003

EXTENSIONS

Corrected and extended by Ryan Propper, Jun 19 2005

STATUS

approved

A090518

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

+10
4

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Conjecture: No term is zero.

LINKS

Table of n, a(n) for n=1..19.

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

CROSSREFS

Cf. A090517, A090519, A090520.

KEYWORD

base,nonn

AUTHOR

Amarnath Murthy, Dec 07 2003

EXTENSIONS

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

STATUS

approved

A090517

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

+10
3

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..65.

EXAMPLE

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

MATHEMATICA

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

CROSSREFS

Cf. A090518, A090519, A090520.

KEYWORD

base,nonn

AUTHOR

Amarnath Murthy, Dec 07 2003

EXTENSIONS

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

Further terms from David Wasserman, Dec 20 2005

STATUS

approved

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