A125308 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.

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

1,1

Comments

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A010051, A007628 (reflectable emirps).

Sequence in context: A023248 A199341 A111488 * A260044 A199303 A244047

Adjacent sequences: A125305 A125306 A125307 * A125309 A125310 A125311

Keyword

easy,nonn,base

Author

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

Extensions

More terms from Arkadiusz Wesolowski, Mar 06 2013

Status

approved