A345728 Primes with an odd number of digits and 0 as the middle digit.

101, 103, 107, 109, 307, 401, 409, 503, 509, 601, 607, 701, 709, 809, 907, 10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 11003, 11027, 11047, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 12007, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097, 13001, 13003, 13007

Offset: 1

Author

James S. DeArmon, Jun 27 2021

Keywords

• nonn
• base

Crossrefs

Cf. A000040 (primes), A134809 (Cyclops primes).

Programs

Mathematica

Select[Prime@Range@2000,OddQ[d=Length[s=IntegerDigits[#]]]&&s[[Ceiling[d/2]]]==0&] (* Giorgos Kalogeropoulos, Jul 04 2021 *)

PARI

isok(p) = {if (isprime(p), my(d=digits(p)); (#d % 2) && (d[#d\2+1] == 0););} \\ Michel Marcus, Jun 28 2021

Perl

#!/usr/bin/perl
$str = "";
foreach $cand (101..20000){  # loop over candidates
    next unless &isPrime($cand);  # is $cand prime? 0/1 result
    @a = split("",$cand);
    next if @a/2 == int @a/2;
    $mid = int @a/2;
    next unless $a[$mid] == 0;
    $str .= "$cand, ";
}
chop $str; chop $str;
print "$str\n";

Python

from sympy import isprime
from itertools import product
def agen(maxdigits):
    for digits in range(3, maxdigits+1, 2):
        for first in "123456789":
            for left in product("0123456789", repeat=digits//2-1):
                left = "".join(left)
                for right in product("0123456789", repeat=digits//2-1):
                    right = "".join(right)
                    for last in "1379":
                        t = int("".join(first + left + "0" + right + last))
                        if isprime(t): yield t
print([an for an in agen(5)]) # Michael S. Branicky, Jun 28 2021