A321806 Number of zeros in palindromic strings of the form '123456789'|'1...0...1'|'987654321' whose decimal expansions are primes (palindromic).

7, 11, 19, 571, 829

Offset: 1

Author

Mikk Heidemaa, Nov 19 2018

Keywords

• nonn
• base
• hard
• more

Comments

Also numbers k such that 1234567891*10^(k+10) + 1987654321 is prime.

a(1)-a(5) are themselves primes i.e. numbers of (central) zeros in these palindromic strings (the decimal expansions of which are primes) are also primes.

If a(6) exists then it is >40000 (if it is composite) or >60000 (if it is prime).

Examples

			a(1)=7 because the decimal expansion of the palindromic string '123456789100000001987654321' (concatenation of the prefix '123456789', the central string '100000001', and the suffix '987654321') is prime (palindromic) containing 7 zeros.
a(2)=11 as the decimal expansion of '1234567891000000000001987654321' is prime which contains 11 zeros.
		

Crossrefs

Cf. A002385.

Programs

Mathematica

ParallelMap[If[PrimeQ[1234567891*10^(#+10)[phone]], #, Nothing] &, Range@1000]

Perl

use ntheory "is_prime"; do { print "$\n" if is_prime("1234567891" . "0"x$ . "1987654321") } for 1..2000; # Dana Jacobsen, Nov 21 2018