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

Author

G. L. Honaker, Jr.

Keywords

• base
• nonn
• easy
• nice

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]

Crossrefs

Cf. A007597, A006567, A046732.

Programs

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

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 *)

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

Extensions

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