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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
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
easy,nonn,base
AUTHOR
G. L. Honaker, Jr., Dec 10 2006
EXTENSIONS
More terms from Arkadiusz Wesolowski, Mar 06 2013
STATUS
approved

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Last modified June 14 02:27 EDT 2024. Contains 373392 sequences. (Running on oeis4.)