A059496 a(1) = 2; a(n+1) is obtained by and trying to change just one digit of a(n), starting with the least significant digit, until a new prime is reached. Take the lexicographically earliest sequence. Digits may be replaced by any nonzero digit.

2, 3, 5, 7, 17, 11, 13, 19, 29, 23, 43, 41, 47, 37, 31, 61, 67, 97, 197, 191, 193, 199, 139, 131, 137, 127, 157, 151, 181, 281, 283, 223, 227, 229, 239, 233, 263, 269, 569, 563, 523, 521, 541, 547, 557, 577, 571, 271, 277, 257, 251, 211, 241, 641, 643, 647, 617, 613, 619

Offset: 1

Author

David W. Wilson, Feb 05 2001

Keywords

• nonn
• base
• nice
• fini
• full

Comments

The sequence is finite with last term a(114) = 149, see link and b-file. - Reinhard Zumkeller, Jan 06 2014

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..114
• Reinhard Zumkeller, Proof of finiteness

Crossrefs

Another decimal analog of A059458. See A059497 for primes that are missed. Cf. A059471, A059498.

Cf. A010051.

Programs

Haskell

a059496 n = a059496_list !! (n-1)
a059496_list = 2 : f [2] [2] where
   f qs xs = g candidates where
     g [] = []
     g (ys:yss) | a010051 q == 0 || q `elem` qs = g yss
                | otherwise = q : f (q:qs) ys
                where q = foldr (\d r -> 10 * r + d) 0 ys
     candidates = [us ++ [z] ++ vs | i <- [0 .. length xs - 1],
                         let (us, (_:vs)) = splitAt i xs, z <- [1..9]] ++
                  [xs ++ [z] | z <- [1..9]]
-- Reinhard Zumkeller, Jan 06 2014