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
Examples
101 yields only one prime using digit '6' -> 1(6)0(6)1 -> prime 16061.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Programs
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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
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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 *)
Extensions
Offset corrected by Reinhard Zumkeller, May 07 2013