login
Total number of palindromic primes in base 6 with n digits.
1

%I #19 Dec 07 2015 01:04:28

%S 3,1,6,0,21,0,95,0,445,0,2181,0,11496,0,59723,0,315949,0,1718494,0,

%T 9403664,0

%N Total number of palindromic primes in base 6 with n digits.

%C Every palindrome with an even number of digits is divisible by 11 (in base 6) and therefore is composite (not prime). Hence there is only one palindromic prime with an even number of digits.

%C A palindromic prime > 3 in base 6 must start (and end) with either the digit 1 or the digit 5. - _Chai Wah Wu_, Dec 03 2015

%H Eric Weisstein: <a href="http://mathworld.wolfram.com/PalindromicPrime.html">Palindromic Prime</a>.

%e a(2) = 1, because 11(6) = 7(10), is the only palindromic prime with 2 digits. - _Michel Marcus_, Oct 11 2014

%t Length@ Select[Prime@ Range[PrimePi[6^# + 1], PrimePi[6^(# + 1)]], # == Reverse@ # &@ IntegerDigits[#, 6] &] & /@ Range[0, 8] (* _Michael De Vlieger_, Dec 06 2015 *)

%o (PARI) a(nd, b=6) = {if ((nd > 2) && ((nd % 2) == 0), return (0)); nb = 0; forprime(p = b^(nd-1), b^nd-1, d = digits(p, b); if (Pol(d) == Polrev(d), nb++);); nb;} \\ _Michel Marcus_, Oct 11 2014

%Y Cf. A029974, A117701.

%K nonn,base,more

%O 1,1

%A _Martin Renner_, Apr 15 2006

%E a(11)-a(12) from _Michel Marcus_, Oct 11 2014

%E a(13)-a(22) from _Chai Wah Wu_, Dec 03 2015