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

0,3

Comments

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

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

Links

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

Example

.    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  .

Mathematica

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

Prog

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

Crossrefs

Cf. A007088, A030308, A031298, A080719.

Sequence in context: A303605 A266946 A081551 * A007088 A115848 A136814

Adjacent sequences: A257828 A257829 A257830 * A257832 A257833 A257834

Keyword

nonn,base

Author

Reinhard Zumkeller, May 10 2015

Status

approved