A117785 - OEIS

%I #13 Feb 16 2025 08:33:00

%S 4,4,17,17,64,64,375,375,2319,2319,15130,15130,99554,99554,675166,

%T 675166,4753617,4753617,33752394,33752394,239605153,239605153

%N Total number of palindromic primes in base 8 below 8^n.

%C Every palindrome with an even number of digits is divisible by 11 (in base 8) and therefore is composite (not prime). Hence there is no palindromic prime with an even number of digits.

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

%p revdigs:= proc(n) local L,i;

%p   L:= convert(n,base,8);

%p   add(L[-i]*8^(i-1),i=1..nops(L))

%p end proc:

%p f:= proc(d) local x,y;

%p      nops(select(isprime, [seq(seq(x*8^(d+1)+y*8^d+revdigs(x), y=0..7),x=8^(d-1)..8^d-1)]));

%p end proc:

%p T:= ListTools:-PartialSums([4, op(map(f,[$1..6]))]):

%p map(t -> (t,t), T); # _Robert Israel_, Aug 01 2019

%Y Cf. A029976, A006341.

%Y Partial sums of A117786.

%K nonn,base,more

%O 1,1

%A _Martin Renner_, Apr 15 2006

%E a(9)-a(22) from _Robert Israel_, Aug 01 2019, using data from A117786.