OFFSET
1,1
COMMENTS
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.
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
LINKS
Eric Weisstein: Palindromic Prime.
EXAMPLE
a(2) = 1, because 11(6) = 7(10), is the only palindromic prime with 2 digits. - Michel Marcus, Oct 11 2014
MATHEMATICA
Length@ Select[Prime@ Range[PrimePi[6^# + 1], PrimePi[6^(# + 1)]], # == Reverse@ # &@ IntegerDigits[#, 6] &] & /@ Range[0, 8] (* Michael De Vlieger, Dec 06 2015 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Martin Renner, Apr 15 2006
EXTENSIONS
a(11)-a(12) from Michel Marcus, Oct 11 2014
a(13)-a(22) from Chai Wah Wu, Dec 03 2015
STATUS
approved