A237851 a(1)=1; a(n) is the smallest integer not yet in the sequence divisible by all nonzero digits of a(n-1).

1, 2, 4, 8, 16, 6, 12, 10, 3, 9, 18, 24, 20, 14, 28, 32, 30, 15, 5, 25, 40, 36, 42, 44, 48, 56, 60, 54, 80, 64, 72, 70, 7, 21, 22, 26, 66, 78, 112, 34, 84, 88, 96, 90, 27, 98, 144, 52, 50, 35, 45, 100, 11, 13, 33, 39, 63, 102, 38, 120, 46, 108, 104, 68, 168

Offset: 1

Author

Eric Angelini, Feb 14 2014

Keywords

• nonn
• base
• nice
• look

Comments

A permutation of the naturals with inverse A237860.

If a(n) is a prime greater than 7 then no digit of a(n-1) is greater than 1, cf. A007088.

Links

• Lars Blomberg and Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A002796, A180410, A002473, A237860, A007088.

Programs

Haskell

import Data.List (nub, sort, delete)
a237851 n = a237851_list !! (n-1)
a237851_list = 1 : f 1 [2..] where
   f x zs = g zs where
     g (u:us) | all ((== 0) . (mod u)) ds = u : f u (delete u zs)
              | otherwise = g us
              where ds = dropWhile (<= 1) $
                         sort $ nub $ map (read . return) $ show x
-- Reinhard Zumkeller, Feb 14 2014

Mathematica

a[1] = 1;
a[n_] := a[n] = For[k = 1, True, k++, If[FreeQ[Array[a, n-1], k], If[ AllTrue[Select[IntegerDigits[a[n-1]], #>0&] // Union, Divisible[k, #]&], Return[k]]]];
a /@ Range[100] (* Jean-François Alcover, Nov 26 2019 *)