A117782 Total number of palindromic primes in base 6 with n digits.

3, 1, 6, 0, 21, 0, 95, 0, 445, 0, 2181, 0, 11496, 0, 59723, 0, 315949, 0, 1718494, 0, 9403664, 0

Offset: 1

Author

Martin Renner, Apr 15 2006

Keywords

• nonn
• base
• more

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

Examples

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

Links

• Eric Weisstein: Palindromic Prime.

Crossrefs

Cf. A029974, A117701.

Programs

Mathematica

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

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

Extensions

a(11)-a(12) from Michel Marcus, Oct 11 2014

a(13)-a(22) from Chai Wah Wu, Dec 03 2015