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

1,1

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P. Giannopoulos, The Brainteasers, unpublished.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)

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 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

Crossrefs

Cf. A007597, A057770, A080789.

Sequence in context: A139602 A080789 A057770 * A363023 A248802 A290078

Adjacent sequences: A080785 A080786 A080787 * A080789 A080790 A080791

Keyword

base,easy,nonn

Author

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

Extensions

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

Status

approved