A006341 -id:A006341 - cp's OEIS frontend

A029976 Palindromic primes in base 8.

2, 3, 5, 7, 73, 89, 97, 113, 211, 227, 251, 349, 373, 463, 479, 487, 503, 4289, 4481, 4937, 5393, 5521, 5657, 5849, 6761, 7537, 7993, 12547, 12611, 12739, 13003, 13259, 13331, 13523, 14107, 14563, 14627, 14891, 15083, 15667, 15731, 15859

Offset: 1

Patrick De Geest

Chai Wah Wu, Table of n, a(n) for n = 1..15000
Patrick De Geest, World!Of Palindromic Primes

Cf. A006341.

palQ[n_, b_:10] := Module[{idn = IntegerDigits[n, b]}, idn == Reverse[idn]]; Select[Prime[Range[2000]], palQ[#, 8] &] (* Harvey P. Dale, Dec 23 2013 *)

forprime(p=2,10^4, my(d=digits(p,8)); if(d==Vecrev(d),print1(p,", "))); \\ Joerg Arndt, Aug 17 2014

from itertools import chain
from sympy import isprime
from gmpy2 import digits
A029976 = sorted((n for n in chain((int(digits(x,8)+digits(x,8)[::-1],8) for x in range(1,8**6)),(int(digits(x,8)+digits(x,8)[-2::-1],8) for x in range(1,8**6))) if isprime(n)))
# Chai Wah Wu, Aug 16 2014

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

Original entry on oeis.org

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

Offset: 1

Martin Renner, Apr 15 2006

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.

Eric Weisstein: Palindromic Prime.

Cf. A029976, A006341.

Partial sums of A117786.

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

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

A117786 Total number of palindromic primes in base 8 with n digits.

Original entry on oeis.org

4, 0, 13, 0, 47, 0, 311, 0, 1944, 0, 12811, 0, 84424, 0, 575612, 0, 4078451, 0, 28998777, 0, 205852759, 0

Offset: 1

Martin Renner, Apr 15 2006

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.

Eric Weisstein: Palindromic Prime.

Cf. A029976, A006341.

a(9)-a(22) from Chai Wah Wu, Dec 25 2015

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A029976 Palindromic primes in base 8.

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

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A117786 Total number of palindromic primes in base 8 with n digits.

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