A246398 Smallest number of digits that have to be inserted into or prepended to decimal representation of n, to get a prime.

2, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 2, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 2, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 2, 1

Offset: 0

Author

Reinhard Zumkeller, Nov 13 2014

Keywords

• nonn
• base

Comments

a(n) = 0 iff n is a prime number, a(A000040(n)) = 0;

a(n) = A055642(A062584(n)) - A055642(n).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000040, A055642, A062584, A068164.

Programs

Haskell

a246398 n = a246398_list !! n
a246398_list = f 0 $ map show a000040_list where
   f x pss = (length ps - length xs) :
             f (x + 1) (dropWhile (== xs) pss)
     where ps = head [qs | qs <- pss, isin xs qs]; xs = show x
   isin [] _  = True
   isin _  [] = False
   isin (u:us) vs = not (null ws) && isin us ws
                    where ws = dropWhile (/= u) vs