A050805 Inserting any digit between adjacent digits of prime p never yields another prime.

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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

Cf. A050674-A050719, A050806.

Cf. A010051, A000040.

Sequence in context: A185683 A142753 A142141 * A252135 A157737 A061328

Adjacent sequences: A050802 A050803 A050804 * A050806 A050807 A050808

Keyword

nonn,nice,base

Author

Patrick De Geest, Oct 15 1999

Extensions

Offset corrected by Reinhard Zumkeller, May 07 2013

Status

approved