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

1,1

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).

Links

Table of n, a(n) for n=1..5.

Example

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.

Mathematica

ParallelMap[If[PrimeQ[1234567891*10^(#+10)+1987654321], #, Nothing] &, Range@1000]

Prog

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

Crossrefs

Cf. A002385.

Sequence in context: A319224 A282037 A050562 * A057190 A106674 A184063

Adjacent sequences: A321803 A321804 A321805 * A321807 A321808 A321809

Keyword

nonn,base,hard,more

Author

Mikk Heidemaa, Nov 19 2018

Status

approved