A125308 Primes having only {0, 1, 3, 8} as digits.

3, 11, 13, 31, 83, 101, 103, 113, 131, 181, 311, 313, 331, 383, 811, 881, 883, 1013, 1031, 1033, 1103, 1181, 1301, 1303, 1381, 1801, 1811, 1831, 3001, 3011, 3083, 3181, 3301, 3313, 3331, 3803, 3833, 3881, 8011, 8081, 8101, 8111, 8311, 8803, 8831, 10103

Offset: 1

Author

G. L. Honaker, Jr., Dec 10 2006

Keywords

• easy
• nonn
• base

Comments

Original name: Reflectable primes: those which are invariant upon mirror reflection along the line they are written on. Must contain only the digits 0, 1, 3, or 8.

A rough heuristic argument suggests that there are infinite pairs (n, prime(n)) in which both n and prime(n) are reflectable, like in prime(1101088113338) = 33138318000311. See Links for a table of the first 250 such pairs. - Giovanni Resta, Mar 10 2013

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000
• Prime Glossary, Reflectable prime
• Giovanni Resta, The first 250 reflectable primes whose indices are reflectable.
• Index to entries for primes with digits in a given set

Crossrefs

Cf. A010051, A007628 (reflectable emirps).

Programs

Haskell

import Data.List (intersect)
a125308 n = a125308_list !! (n-1)
a125308_list = 3 : h [1,3] where
   h (u:us) | null (show v `intersect` "245679") &&
              a010051' v == 1 = v : h (us ++ [v])
            | otherwise       = h (us ++ [v])
            where v = u + 10
-- Reinhard Zumkeller, Jul 16 2014

Mathematica

Select[FromDigits /@ Tuples[{0, 1, 3, 8}, 5], PrimeQ[#] &] (* Arkadiusz Wesolowski, Mar 06 2013 *)

Extensions

More terms from Arkadiusz Wesolowski, Mar 06 2013