A050806 Inserting any digit between adjacent digits of prime p produces exactly 1 new prime.

101, 149, 163, 241, 269, 271, 317, 347, 367, 397, 409, 419, 443, 487, 509, 541, 587, 601, 641, 761, 787, 811, 821, 863, 907, 919, 1439, 1481, 1663, 1877, 2089, 2111, 2579, 2593, 2671, 2819, 2971, 3121, 3457, 3463, 3571, 3643, 3659, 3769, 3917, 4001

Offset

1,1

Links

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

Example

101 yields only one prime using digit '6' -> 1(6)0(6)1 -> prime 16061.

Mathematica

aQ[n_]:=Plus@@Boole[PrimeQ[Table[FromDigits[Riffle[IntegerDigits[n], k]], {k, 0, 9}]]]==1; Select[Prime[Range[5, 555]], aQ[#]&] (* Jayanta Basu, May 30 2013 *)

Prog

(Haskell)
import Data.List (intersperse)
a050806 n = a050806_list !! (n-1)
a050806_list = filter ((== 1) . sum . 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, A050805.

Cf. A010051, A000040.

Sequence in context: A122531 A141871 A238503 * A243890 A129563 A141927

Adjacent sequences: A050803 A050804 A050805 * A050807 A050808 A050809

Keyword

nonn,base

Author

Patrick De Geest, Oct 15 1999

Extensions

Offset corrected by Reinhard Zumkeller, May 07 2013

Status

approved