A257831 In decimal representation of n: replace each digit with its binary representation.

0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 10, 11, 110, 111, 1100, 1101, 1110, 1111, 11000, 11001, 100, 101, 1010, 1011, 10100, 10101, 10110, 10111, 101000, 101001, 110, 111, 1110, 1111, 11100, 11101, 11110, 11111, 111000, 111001, 1000, 1001, 10010, 10011

Offset: 0

Author

Reinhard Zumkeller, May 10 2015

Keywords

• nonn
• base

Comments

a(n) = n iff (largest digit of n) = 1: a(A007088(n)) = A007088(n);

a(n) = A007088(A080719(n)).

Examples

			.    n |  dec    -->  bin         |     a(n) |  A080719(n)
. -----+--------------------------+----------+------------
.  100 |  [1,0,0]  |  [1,0,0]     |     100  |          4
.  101 |  [1,0,1]  |  [1,0,1]     |     101  |          5
.  102 |  [1,0,2]  |  [1,0,10]    |    1010  |         10
.  103 |  [1,0,3]  |  [1,0,11]    |    1011  |         11
.  104 |  [1,0,4]  |  [1,0,100]   |   10100  |         20
.  105 |  [1,0,5]  |  [1,0,101]   |   10101  |         21
.  106 |  [1,0,6]  |  [1,0,110]   |   10110  |         22
.  107 |  [1,0,7]  |  [1,0,111]   |   10111  |         23
.  108 |  [1,0,8]  |  [1,0,1000]  |  101000  |         40
.  109 |  [1,0,9]  |  [1,0,1001]  |  101001  |         41
.  110 |  [1,1,0]  |  [1,1,0]     |     110  |          6
.  111 |  [1,1,1]  |  [1,1,1]     |     111  |          7
.  112 |  [1,1,2]  |  [1,1,10]    |    1110  |         14
.  113 |  [1,1,3]  |  [1,1,11]    |    1111  |         15
.  114 |  [1,1,4]  |  [1,1,100]   |   11100  |         28
.  115 |  [1,1,5]  |  [1,1,101]   |   11101  |         29
.  116 |  [1,1,6]  |  [1,1,110]   |   11110  |         30
.  117 |  [1,1,7]  |  [1,1,111]   |   11111  |         31
.  118 |  [1,1,8]  |  [1,1,1000]  |  111000  |         56
.  119 |  [1,1,9]  |  [1,1,1001]  |  111001  |         57
.  120 |  [1,2,0]  |  [1,10,0]    |    1100  |         12
.  121 |  [1,2,1]  |  [1,10,1]    |    1101  |         13
.  122 |  [1,2,2]  |  [1,10,10]   |   11010  |         26
.  123 |  [1,2,3]  |  [1,10,11]   |   11011  |         27
.  124 |  [1,2,4]  |  [1,10,100]  |  110100  |         52
.  125 |  [1,2,5]  |  [1,10,101]  |  110101  |         53  .
		

Links

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

Crossrefs

Cf. A007088, A030308, A031298, A080719.

Programs

Haskell

import Data.Maybe (mapMaybe)
a257831 = foldr (\b v -> 10 * v + b) 0 .
           concat . mapMaybe (flip lookup bin) . a031298_row
            where bin = zip [0..9] a030308_tabf

Mathematica

Table[FromDigits[Flatten[IntegerDigits[#,2]&/@IntegerDigits[n]]],{n,0,50}] (* Harvey P. Dale, Jun 06 2020 *)

Python

def A257831(n):
    return int(''.join((format(int(d),'b') for d in str(n))))
# Chai Wah Wu, May 10 2015