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A064490 Smallest prime with prime(n) decimal digits.

%I A064490 #36 Jul 02 2025 16:02:01
%S A064490 11,101,10007,1000003,10000000019,1000000000039,10000000000000061,
%T A064490 1000000000000000003,10000000000000000000009,
%U A064490 10000000000000000000000000331,1000000000000000000000000000057,1000000000000000000000000000000000067,10000000000000000000000000000000000000121
%N A064490 Smallest prime with prime(n) decimal digits.
%H A064490 Alois P. Heinz, <a href="/A064490/b064490.txt">Table of n, a(n) for n = 1..168</a> (first 75 terms from Harry J. Smith)
%F A064490 a(n) = A003617(A000040(n)).
%F A064490 a(n) = A000040(A064489(n)).
%e A064490 11 is the first prime with 2 decimal digits.
%e A064490 101 is the first prime with 3 decimal digits.
%p A064490 for n from 1 to 20 do p := ithprime(n): for i from 10^(p-1) to 10^p do if isprime(i) then printf(`%d,`,i); break; fi: od: od:
%p A064490 # second Maple program:
%p A064490 a:= n-> nextprime(10^(ithprime(n)-1)):
%p A064490 seq(a(n), n=1..15);  # _Alois P. Heinz_, Jun 24 2018
%t A064490 Table[NextPrime[10^(n-1)],{n,Prime[Range[15]]}] (* _Harvey P. Dale_, Feb 06 2020 *)
%o A064490 (PARI) l(n)=ln=0; while(n,n=floor(n/10); ln++); return(ln);
%o A064490 a=0; for(n=1,10^6,x=l(prime(n)); if(isprime(x),b=x; if(b>a,a=b; print(prime(n)))))
%o A064490 (PARI) { for (n=1, 75, p=prime(n); a=nextprime(10^(p - 1)); write("b064490.txt", n, " ", a) ) } \\ _Harry J. Smith_, Sep 16 2009
%o A064490 (Python)
%o A064490 from sympy import prime, nextprime, primepi
%o A064490 def a(n): return nextprime(10**(prime(n)-1))
%o A064490 print([a(n) for n in range(1, 14)]) # _Michael S. Branicky_, May 26 2021
%Y A064490 Cf. A000040, A003617, A064489.
%K A064490 base,nonn
%O A064490 1,1
%A A064490 _Jason Earls_, Oct 04 2001
%E A064490 More terms from _James Sellers_, Oct 08 2001
%E A064490 Offset changed from 0 to 1 by _Harry J. Smith_, Sep 16 2009