A057436 Contains digits 1 through 6 only.

1, 2, 3, 4, 5, 6, 11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66, 111, 112, 113, 114, 115, 116, 121, 122, 123, 124, 125, 126, 131, 132, 133, 134, 135, 136, 141, 142, 143

Offset: 1

Author

Thomas Schulze (jazariel(AT)tiscalenet.it), Sep 08 2000

Keywords

• easy
• nice
• nonn
• base

Comments

Numbers whose digits can be generated by successively throwing a regular die with the numbers 1..6 and concatenating the results.

Examples

			The number 61 can be generated by throwing a die twice and combining the results, but 17 not.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A007092, A214676.

Programs

Haskell

import Data.List (intersect)
a057436 n = a057436_list !! (n-1)
a057436_list = filter (null . (intersect "0789") . show) [1..]
-- Reinhard Zumkeller, Mar 28 2012

Mathematica

Select[Range[200],Max[IntegerDigits[#]]<=6&& DigitCount[#,10,0] ==0&]  (* Harvey P. Dale, Apr 04 2011 *)
FromDigits/@Flatten[Table[Tuples[Range[6],n],{n,3}],1] (* Harvey P. Dale, Jul 26 2015 *)

Python

from itertools import product
A057436_list = [int(''.join(d)) for l in range(1,5) for d in product('123456',repeat=l)] # Chai Wah Wu, Sep 01 2021

Formula

a(n+1) = 1 + (if a(n) mod 10 < 6 then a(n) else a(a(n)\10)*10), a(0)=1. - Reinhard Zumkeller, Jul 13 2007

Extensions

Offset corrected by Reinhard Zumkeller, Aug 16 2011