A117785 Total number of palindromic primes in base 8 below 8^n.

4, 4, 17, 17, 64, 64, 375, 375, 2319, 2319, 15130, 15130, 99554, 99554, 675166, 675166, 4753617, 4753617, 33752394, 33752394, 239605153, 239605153

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 8) and therefore is composite (not prime). Hence there is no palindromic prime with an even number of digits.

Links

• Eric Weisstein: Palindromic Prime.

Crossrefs

Cf. A029976, A006341.

Partial sums of A117786.

Programs

Maple

revdigs:= proc(n) local L,i;
  L:= convert(n,base,8);
  add(L[-i]*8^(i-1),i=1..nops(L))
end proc:
f:= proc(d) local x,y;
     nops(select(isprime, [seq(seq(x*8^(d+1)+y*8^d+revdigs(x), y=0..7),x=8^(d-1)..8^d-1)]));
end proc:
T:= ListTools:-PartialSums([4, op(map(f,[$1..6]))]):
map(t -> (t,t), T); # Robert Israel, Aug 01 2019

Extensions

a(9)-a(22) from Robert Israel, Aug 01 2019, using data from A117786.