A048890 Primes that yield a different prime when rotated by 180 degrees.

19, 61, 109, 199, 601, 661, 1019, 1061, 1091, 1109, 1181, 1601, 1609, 1669, 1699, 1811, 1901, 1999, 6011, 6091, 6101, 6199, 6619, 6661, 6689, 6691, 6899, 6991, 10061, 10069, 10091, 10691, 10861, 10909, 11069, 11681, 11909, 16001, 16619, 16661

Offset

1,1

Comments

Also called invertible primes. [Lekraj Beedassy, Jan 03 2009]

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

C. K. Caldwell, The Prime Glossary, strobogrammatic [Lekraj Beedassy, Jan 03 2009]

Mathematica

lst = {}; fQ[n_] := Block[{allset = {0, 1, 6, 8, 9}, id = IntegerDigits@n}, rid = Reverse[id /. {6 -> 9, 9 -> 6}]; Union@ Join[id, allset] == allset && PrimeQ@ FromDigits@ rid && rid != id]; Do[ If[ PrimeQ@n && fQ@n, AppendTo[lst, n]], {n, 16900}]; lst (* Robert G. Wilson v, Feb 27 2007 *)

Prog

(Haskell)
import Data.List (unfoldr)
a048890 n = a048890_list !! (n-1)
a048890_list = filter f a000040_list where
   f x = all (`elem` [0, 1, 6, 8, 9]) ds && x' /= x && a010051 x' == 1
     where x' = foldl c 0 ds
           c v 6 = 10*v + 9; c v 9 = 10*v + 6; c v d = 10*v + d
           ds = unfoldr d x
           d z = if z == 0 then Nothing else Just $ swap $ divMod z 10
-- Reinhard Zumkeller, Nov 18 2011
(Python)
from itertools import product
from sympy import isprime
A048890_list = []
for d in product('01689', repeat=6):
    s = ''.join(d)
    p = int(s)
    if p > 0:
        q = int(s[::-1].rstrip('0').translate(''.maketrans('69', '96')))
        if p != q and isprime(q) and isprime(p):
            A048890_list.append(p) # Chai Wah Wu, Sep 13 2021

Crossrefs

Cf. A007597, A006567, A046732.

Sequence in context: A158521 A141897 A031384 * A127854 A338299 A092327

Adjacent sequences: A048887 A048888 A048889 * A048891 A048892 A048893

Keyword

base,nonn,easy,nice

Author

G. L. Honaker, Jr.

Extensions

Better definition and more terms from Robert G. Wilson v, Feb 27 2007

Status

approved