A048890 - OEIS

%I #27 Apr 03 2023 10:36:09

%S 19,61,109,199,601,661,1019,1061,1091,1109,1181,1601,1609,1669,1699,

%T 1811,1901,1999,6011,6091,6101,6199,6619,6661,6689,6691,6899,6991,

%U 10061,10069,10091,10691,10861,10909,11069,11681,11909,16001,16619,16661

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

%C Also called invertible primes. [_Lekraj Beedassy_, Jan 03 2009]

%H Reinhard Zumkeller, <a href="/A048890/b048890.txt">Table of n, a(n) for n = 1..1000</a>

%H C. K. Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/page.php?sort=Strobogrammatic">strobogrammatic</a> [_Lekraj Beedassy_, Jan 03 2009]

%t 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 *)

%o (Haskell)

%o import Data.List (unfoldr)

%o a048890 n = a048890_list !! (n-1)

%o a048890_list = filter f a000040_list where

%o    f x = all (`elem` [0,1,6,8,9]) ds && x' /= x && a010051 x' == 1

%o      where x' = foldl c 0 ds

%o            c v 6 = 10*v + 9; c v 9 = 10*v + 6; c v d = 10*v + d

%o            ds = unfoldr d x

%o            d z = if z == 0 then Nothing else Just $ swap $ divMod z 10

%o -- _Reinhard Zumkeller_, Nov 18 2011

%o (Python)

%o from itertools import product

%o from sympy import isprime

%o A048890_list = []

%o for d in product('01689',repeat=6):

%o     s = ''.join(d)

%o     p = int(s)

%o     if p > 0:

%o         q = int(s[::-1].rstrip('0').translate(''.maketrans('69','96')))

%o         if p != q and isprime(q) and isprime(p):

%o             A048890_list.append(p) # _Chai Wah Wu_, Sep 13 2021

%Y Cf. A007597, A006567, A046732.

%K base,nonn,easy,nice

%O 1,1

%A _G. L. Honaker, Jr._

%E Better definition and more terms from _Robert G. Wilson v_, Feb 27 2007