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
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
- C. K. Caldwell, The Prime Glossary, strobogrammatic [_Lekraj Beedassy_, Jan 03 2009]
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
Comments