A264662 Triangle read by rows: row n contains the first n primes in lexicographical order of their mirrored binary representation.

2, 2, 3, 2, 5, 3, 2, 5, 3, 7, 2, 5, 3, 11, 7, 2, 5, 13, 3, 11, 7, 2, 17, 5, 13, 3, 11, 7, 2, 17, 5, 13, 3, 19, 11, 7, 2, 17, 5, 13, 3, 19, 11, 7, 23, 2, 17, 5, 13, 29, 3, 19, 11, 7, 23, 2, 17, 5, 13, 29, 3, 19, 11, 7, 23, 31, 2, 17, 5, 37, 13, 29, 3, 19, 11

Offset

1,1

Comments

T(n,A263856(n)) = A000040(n): A263856(n) = index of prime(n) in n-th row.

Links

Reinhard Zumkeller, Rows n = 1..250 of triangle, flattened

Example

.   n |   T(n,k), k=1..n
. ----+-----------------------------------------------------------------
.   1 | 2                          01
.   2 | 2  3                       01 11
.   3 | 2  5  3                    01 101   11
.   4 | 2  5  3  7                 01 101   11   111
.   5 | 2  5  3 11  7              01 101   11   1101 111
.   6 | 2  5 13  3 11  7           01 101   1011 11   1101 111
.   7 | 2 17  5 13  3 11  7        01 10001 101  1011 11   1101  111
.   8 | 2 17  5 13  3 19 11  7     01 10001 101  1011 11   11001 1101 111
.   9 | 2 17  5 13  3 19 11  7 23
.  10 | 2 17  5 13 29  3 19 11  7 23
.  11 | 2 17  5 13 29  3 19 11  7 23 31
.  12 | 2 17  5 37 13 29  3 19 11  7 23 31
.  13 | 2 17 41  5 37 13 29  3 19 11  7 23 31
.  14 | 2 17 41  5 37 13 29  3 19 11 43 7  23 31
.  15 | 2 17 41  5 37 13 29  3 19 11 43  7 23 47 31
.  16 | 2 17 41  5 37 53 13 29  3 19 11 43  7 23 47 31
.  17 | 2 17 41  5 37 53 13 29  3 19 11 43 59  7 23 47 31
.  18 | 2 17 41  5 37 53 13 29 61  3 19 11 43 59  7 23 47 31
.  19 | 2 17 41  5 37 53 13 29 61  3 67 19 11 43 59  7 23 47 31
.  20 | 2 17 41  5 37 53 13 29 61  3 67 19 11 43 59  7 71 23 47 31

Mathematica

row[n_] := SortBy[Prime[Range[n]], StringJoin[ToString /@ Reverse[IntegerDigits[#, 2]]]&];
Table[row[n], {n, 1, 20}] // Flatten (* Jean-François Alcover, Sep 25 2021 *)

Prog

(Haskell)
import Data.List (inits, sortBy); import Data.Function (on)
a264662 n k = a264662_tabl !! (n-1) !! (n-1)
a264662_row n = a264662_tabl !! (n-1)
a264662_tabl = map (sortBy (compare `on` (reverse . show . a007088))) $
                   tail $ inits a000040_list

Crossrefs

Cf. A263846, A000040, A007088, A007504 (row sums), A264666 (partial row products), A037126 (rows sorted naturally).

Sequence in context: A370834 A076397 A254269 * A076403 A157987 A025478

Adjacent sequences: A264659 A264660 A264661 * A264663 A264664 A264665

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Nov 20 2015

Status

approved