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

1,1

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

Table of n, a(n) for n=1..22.

Eric Weisstein: Palindromic Prime.

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

Crossrefs

Cf. A029976, A006341.

Partial sums of A117786.

Sequence in context: A191972 A101407 A294245 * A117787 A113727 A214141

Adjacent sequences: A117782 A117783 A117784 * A117786 A117787 A117788

Keyword

nonn,base,more

Author

Martin Renner, Apr 15 2006

Extensions

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

Status

approved