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A117785
Total number of palindromic primes in base 8 below 8^n.
6
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.
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
Partial sums of A117786.
Sequence in context: A191972 A101407 A294245 * A117787 A113727 A214141
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