A080788 Primes that are still primes when turned upsided down.

11, 19, 61, 101, 109, 181, 199, 601, 619, 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, 16091

Offset: 1

Author

P. Giannopoulos (pgiannop1(AT)yahoo.com), Mar 12 2003

Keywords

• base
• easy
• nonn

References

• P. Giannopoulos, The Brainteasers, unpublished.

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..11210 (First 1000 terms from Reinhard Zumkeller)

Crossrefs

Cf. A007597, A057770, A080789.

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

Python

from sympy import isprime
from itertools import product
def ud(s):
    return s[::-1].translate({ord('6'):ord('9'), ord('9'):ord('6')})
def auptod(maxdigits):
    alst = []
    for d in range(1, maxdigits+1):
        for p in product("01689", repeat=d-1):
            if d > 1 and p[0] == "0": continue
            for end in "19":
                s = "".join(p) + end
                t, udt = int(s), int(ud(s))
                if isprime(t) and isprime(udt): alst.append(t)
    return alst
print(auptod(5)) # Michael S. Branicky, Nov 19 2021

Extensions

Missing 1669 and 6689 inserted by Reinhard Zumkeller, Nov 18 2011