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

Author

Reinhard Zumkeller, Nov 20 2015

Keywords

• nonn
• tabl

Comments

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

Examples

			.   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
		

Links

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

Crossrefs

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

Programs

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

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 *)