A199328 Palindromic primes in the sense of A007500 with digits '0', '1' and '8' only.

11, 101, 181, 1181, 1811, 18181, 108881, 110881, 118081, 180181, 180811, 181081, 188011, 188801, 1008001, 1088081, 1110881, 1180811, 1181881, 1808801, 1880111, 1880881, 1881811, 1881881, 10001081, 10001801, 10011101, 10080011, 10101181, 10111001, 10111081, 10180801, 10188811, 10808101, 10810001

Offset: 1

Author

M. F. Hasler, Nov 05 2011

Keywords

• nonn
• base

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..10000 (First 4188 terms from Chai Wah Wu.)

Crossrefs

Intersection of A007500 and A061247.

Cf. A020449-A020472, A199325-A199329.

Programs

Mathematica

Select[10#+1&/@FromDigits/@Tuples[{0,1,8},7],AllTrue[{#,IntegerReverse[#]},PrimeQ]&] (* Harvey P. Dale, Mar 28 2025 *)

PARI

a(n=50,L=[0,1,8],show=0)={my(t);for(d=1,1e9,u=vector(d,i,10^(d-i))~;forvec(v=vector(d,i,[1+(i==1&!L[1]),#L]),isprime(t=vector(d,i,L[v[i]])*u)||next;isprime(A004086(t))||next;show&print1(t",");n--||return(t)))}

Python

from itertools import product
from sympy import isprime
A199328_list = [n for n in (int(''.join(s)) for s in product('018',repeat=10)) if isprime(n) and isprime(int(str(n)[::-1]))] # Chai Wah Wu, Dec 17 2015