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A117782
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Total number of palindromic primes in base 6 with n digits.
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1
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3, 1, 6, 0, 21, 0, 95, 0, 445, 0, 2181, 0, 11496, 0, 59723, 0, 315949, 0, 1718494, 0, 9403664, 0
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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a(2) = 1, because 11(6) = 7(10), is the only palindromic prime with 2 digits. - Michel Marcus, Oct 11 2014
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MATHEMATICA
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Length@ Select[Prime@ Range[PrimePi[6^# + 1], PrimePi[6^(# + 1)]], # == Reverse@ # &@ IntegerDigits[#, 6] &] & /@ Range[0, 8] (* Michael De Vlieger, Dec 06 2015 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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