Search: a090518 -id:a090518
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A090519
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Smallest prime p such that floor((10^n)/p) is prime, or 0 if no such number exists.
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+10
5
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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a(5) = 89, as floor((10^5)/89) = 1123 is the largest such prime.
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MAPLE
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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:
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MATHEMATICA
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<<NumberTheory`; Do[k = 2; While[ !PrimeQ[Floor[10^n / k]], k = NextPrime[k]]; Print[k], {n, 1, 50}] (* Ryan Propper, Jun 19 2005 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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5, 7, 43, 769, 1123, 52631, 1428571, 2127659, 14925373, 769230769, 5882352941, 6369426751, 588235294117, 319488817891, 9345794392523, 24449877750611, 662251655629139, 1293661060802069, 67114093959731543, 244498777506112469
(list;
graph;
refs;
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history;
text;
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OFFSET
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1,1
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COMMENTS
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Conjecture: No term is zero.
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LINKS
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PROG
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(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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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A090517
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Least k such that floor[(10^n)/k] is prime.
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+10
3
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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)
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(1) = 2 as 10/2 = 5 is a prime. a(3) = 12 as floor[1000/12] = 83 is prime.
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MATHEMATICA
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lkp[n_]:=Module[{k=2, c=10^n}, While[!PrimeQ[Floor[c/k]], k++]; k]; Array[ lkp, 70] (* Harvey P. Dale, Jul 09 2018 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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Corrected and extended by Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Jan 28 2004
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STATUS
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approved
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