A048889 Composite numbers not ending in zero that yield a prime when turned upside down.

68, 116, 118, 161, 166, 169, 188, 608, 616, 1006, 1018, 1066, 1081, 1096, 1106, 1108, 1118, 1169, 1186, 1606, 1618, 1808, 1816, 1898, 1916, 1918, 1969, 1981, 1988, 1996, 6001, 6008, 6016, 6098, 6188, 6191, 6196, 6616, 6668, 6698, 6808, 6809, 6881, 6896

Offset

1,1

Links

Robert Israel and Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 (a(1) to a(1048) from Reinhard Zumkeller)

Example

68 is not prime, yet when turned upside down gives 89 which is prime.

Maple

N:= 1000: # to get a(1) to a(N)
count:= 0:
for q from 1 while count < N do
  if q mod 5 <> 0 then
    L:= convert(q, base, 5);
    m:= nops(L);
    Lx:= subs(2=6, 3=8, 4=9, L);
    x:= add(Lx[i]*10^(i-1), i=1..m);
    if isprime(x) then next fi;
    Ly:= subs(2=9, 3=8, 4=6, L);
    y:= add(Ly[-i]*10^(i-1), i=1..m);
    if isprime(y) then
      count:= count+1;
      A[count]:= x;
    fi
fi
od:
seq(A[i], i=1..count); # Robert Israel, Jul 11 2016

Mathematica

Select[Range[7000], CompositeQ[#]&&Mod[#, 10]!=0&&SubsetQ[{0, 1, 6, 8, 9}, IntegerDigits[ #]]&&PrimeQ[FromDigits[Reverse[IntegerDigits[#]]/.{6->9, 9->6}]]&] (* Harvey P. Dale, Dec 26 2022 *)

Prog

(Haskell)
import Data.List (intersect)
import Numeric (readInt)
import Data.Char (digitToInt)
a048889 n = a048889_list !! (n-1)
a048889_list = filter f a002808_list where
   f n = n `mod` 10 > 0 &&
         null ("23547" `intersect` show n)  &&
         (a010051 (fst $ head $ readInt 10 (const True) ud $ ns) == 1)
       where ns = reverse $ show n
             ud '6' = 9
             ud '9' = 6
             ud z = digitToInt z
-- Reinhard Zumkeller, Aug 11 2011
(Python)
from itertools import product
from sympy import isprime
A048889_list = [m for m in (int(''.join(d)) for d in product('01689', repeat=6)) if m % 10 and not isprime(m) and isprime(int(str(m)[::-1].translate(''.maketrans('69', '96'))))] # Chai Wah Wu, Sep 14 2021

Crossrefs

Cf. A002808, A010051.

Sequence in context: A039540 A235284 A250765 * A111379 A352298 A364692

Adjacent sequences: A048886 A048887 A048888 * A048890 A048891 A048892

Keyword

base,easy,nonn,nice

Author

G. L. Honaker, Jr.

Status

approved