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A117775
Total number of palindromic primes in base 3 below 3^n.
5
1, 1, 3, 3, 6, 6, 18, 18, 26, 26, 73, 73, 179, 179, 459, 459, 1179, 1179, 3004, 3004, 8111, 8111, 22183, 22183, 60789, 60789, 168641, 168641, 469689, 469689, 1322664, 1322664, 3691761, 3691761, 10390938, 10390938, 29502559, 29502559, 84012658, 84012658, 239417332, 239417332
OFFSET
1,3
COMMENTS
Every palindrome with an even number of digits is divisible by 11 (in base 3) and therefore is composite (not prime). Hence there is no palindromic prime with an even number of digits.
LINKS
Eric Weisstein's World of Mathematics, Palindromic Prime.
FORMULA
a(2*k-1) = a(2*k) for k >= 1. - Bernard Schott, Mar 23 2021
EXAMPLE
a(5) = a(6) = 6 as the six palindromic primes below 3^5 are 2_10 = 2_3, 13_10 = 111_3, 23_10 = 212_3, 151_10 = 12121_3, 173_10 = 20102_3, 233_10 = 22122_3. There are no palindromic primes with 6 digits so a(5) = a(6). - David A. Corneth, Mar 21 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Martin Renner, Apr 15 2006
EXTENSIONS
a(15)-a(42) from the data at A117776 added by Amiram Eldar, Mar 21 2021
STATUS
approved