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%I #7 Sep 25 2021 14:50:23
%S 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,
%T 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,
%U 13,29,3,19,11,7,23,31,2,17,5,37,13,29,3,19,11
%N Triangle read by rows: row n contains the first n primes in lexicographical order of their mirrored binary representation.
%C T(n,A263856(n)) = A000040(n): A263856(n) = index of prime(n) in n-th row.
%H Reinhard Zumkeller, <a href="/A264662/b264662.txt">Rows n = 1..250 of triangle, flattened</a>
%e . n | T(n,k), k=1..n
%e . ----+-----------------------------------------------------------------
%e . 1 | 2 01
%e . 2 | 2 3 01 11
%e . 3 | 2 5 3 01 101 11
%e . 4 | 2 5 3 7 01 101 11 111
%e . 5 | 2 5 3 11 7 01 101 11 1101 111
%e . 6 | 2 5 13 3 11 7 01 101 1011 11 1101 111
%e . 7 | 2 17 5 13 3 11 7 01 10001 101 1011 11 1101 111
%e . 8 | 2 17 5 13 3 19 11 7 01 10001 101 1011 11 11001 1101 111
%e . 9 | 2 17 5 13 3 19 11 7 23
%e . 10 | 2 17 5 13 29 3 19 11 7 23
%e . 11 | 2 17 5 13 29 3 19 11 7 23 31
%e . 12 | 2 17 5 37 13 29 3 19 11 7 23 31
%e . 13 | 2 17 41 5 37 13 29 3 19 11 7 23 31
%e . 14 | 2 17 41 5 37 13 29 3 19 11 43 7 23 31
%e . 15 | 2 17 41 5 37 13 29 3 19 11 43 7 23 47 31
%e . 16 | 2 17 41 5 37 53 13 29 3 19 11 43 7 23 47 31
%e . 17 | 2 17 41 5 37 53 13 29 3 19 11 43 59 7 23 47 31
%e . 18 | 2 17 41 5 37 53 13 29 61 3 19 11 43 59 7 23 47 31
%e . 19 | 2 17 41 5 37 53 13 29 61 3 67 19 11 43 59 7 23 47 31
%e . 20 | 2 17 41 5 37 53 13 29 61 3 67 19 11 43 59 7 71 23 47 31
%t row[n_] := SortBy[Prime[Range[n]], StringJoin[ToString /@ Reverse[IntegerDigits[#, 2]]]&];
%t Table[row[n], {n, 1, 20}] // Flatten (* _Jean-François Alcover_, Sep 25 2021 *)
%o (Haskell)
%o import Data.List (inits, sortBy); import Data.Function (on)
%o a264662 n k = a264662_tabl !! (n-1) !! (n-1)
%o a264662_row n = a264662_tabl !! (n-1)
%o a264662_tabl = map (sortBy (compare `on` (reverse . show . a007088))) $
%o tail $ inits a000040_list
%Y Cf. A263846, A000040, A007088, A007504 (row sums), A264666 (partial row products), A037126 (rows sorted naturally).
%K nonn,tabl
%O 1,1
%A _Reinhard Zumkeller_, Nov 20 2015
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