A120533 - OEIS

%I #23 Dec 27 2023 11:58:02

%S 11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,

%T 103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,

%U 193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283

%N Primes having a prime number of digits.

%C Before the 20th century, this sequence would have contained the numbers 1,2,3,5,7; see A008578.

%C There are a total of 8527 terms for primes with 2, 3, or 5 digits, and a total of 594608 terms if primes with 7 digits are also included. - _Harvey P. Dale_, Nov 02 2020

%H Jeppe Stig Nielsen, <a href="/A120533/b120533.txt">Table of n, a(n) for n = 1..10000</a>

%e 10007 is a 5-digit prime and so belongs to the sequence.

%t Table[Prime[Range[PrimePi[10^(p-1)]+1,PrimePi[10^p]]],{p,Prime[Range[ 3]]}]//Flatten (* _Harvey P. Dale_, Nov 02 2020 *)

%o (PARI) g(n) = forprime(x=11,n,if(isprime(length(Str(x))),print1(x",")))

%o (PARI) forprime(p=2,5,forprime(q=10^(p-1),10^p,print1(q", "))) \\ _Charles R Greathouse IV_, Oct 04 2011

%o (Python)

%o from itertools import islice

%o from sympy import isprime, nextprime

%o def agen(): # generator of terms

%o     d = 2

%o     while True:

%o         yield from (i for i in range(10**(d-1)+1, 10**d, 2) if isprime(i))

%o         d = nextprime(d)

%o print(list(islice(agen(), 57))) # _Michael S. Branicky_, Dec 27 2023

%Y Cf. A000040, A124888.

%K base,nonn

%O 1,1

%A _Cino Hilliard_, Aug 06 2006

%E Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 21 2007