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

1,1

Links

Table of n, a(n) for n=1..48.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A183087 A056709 A243825 * A309488 A134809 A256186

Adjacent sequences: A345725 A345726 A345727 * A345729 A345730 A345731

Keyword

nonn,base

Author

James S. DeArmon, Jun 27 2021

Status

approved