A125308 - OEIS

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

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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") &&