login
A050805
Inserting any digit between adjacent digits of prime p never yields another prime.
3
439, 853, 1013, 1061, 1109, 1117, 1153, 1187, 1213, 1249, 1259, 1283, 1291, 1301, 1303, 1361, 1427, 1451, 1489, 1511, 1523, 1531, 1583, 1597, 1607, 1657, 1733, 1747, 1753, 1801, 1873, 1879, 1913, 1951, 2069, 2083, 2137, 2243, 2251, 2267, 2293, 2297
OFFSET
1,1
LINKS
EXAMPLE
40309, 41319, 42327, 43339, 44349, 45359, 46369, 47379, 48389, and 49399 are all composite. Thus, 439, being prime, belongs to the sequence.
MATHEMATICA
a[n_]:=Or@@PrimeQ[Table[FromDigits[Riffle[IntegerDigits[n], k]], {k, 0, 9}]]; Select[Prime[Range[5, 350]], a[#]==False&] (* Jayanta Basu, May 30 2013 *)
Select[Prime[Range[400]], NoneTrue[Table[FromDigits[Riffle[ IntegerDigits[ #], d]], {d, 0, 9}], PrimeQ]&] (* Harvey P. Dale, Aug 04 2021 *)
PROG
(Haskell)
import Data.List (intersperse)
a050805 n = a050805_list !! (n-1)
a050805_list = filter ((all (== 0)) . f) a000040_list where
f p = map (i $ show p) "0123456789"
i ps d = a010051' (read $ intersperse d ps :: Integer)
-- Reinhard Zumkeller, May 07 2013
CROSSREFS
KEYWORD
nonn,nice,base
AUTHOR
Patrick De Geest, Oct 15 1999
EXTENSIONS
Offset corrected by Reinhard Zumkeller, May 07 2013
STATUS
approved