A256946 Irregular triangle where n-th row is integers from 1 to n*(n+2), sorted with first squares in order, then remaining numbers by fractional part of the square root.
1, 2, 3, 1, 4, 5, 2, 6, 7, 3, 8, 1, 4, 9, 10, 5, 11, 2, 6, 12, 13, 7, 3, 14, 8, 15, 1, 4, 9, 16, 17, 10, 5, 18, 11, 19, 2, 6, 12, 20, 21, 13, 7, 22, 3, 14, 23, 8, 15, 24, 1, 4, 9, 16, 25, 26, 17, 10, 27, 5, 18, 28, 11, 19, 29, 2, 6, 12, 20, 30, 31, 21, 13, 7, 32, 22, 3, 14, 33, 23, 8, 34, 15, 24, 35
Offset: 1
Examples
The table starts: 1 2 3 1 4 5 2 6 7 3 8 1 4 9 10 5 11 2 6 12 13 7 3 14 8 15 1 4 9 16 17 10 5 18 11 19 2 6 12 20 21 13 7 22 3 14 23 8 15 24
Links
- Franklin T. Adams-Watters, Table of n, a(n) for n = 1..10385 (Rows 1 to 30, flattened.)
Programs
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Haskell
import Data.List (sortBy); import Data.Function (on) a256946 n k = a256946_tabf !! (n-1) !! (k-1) a256946_row n = a256946_tabf !! (n-1) a256946_tabf = f 0 [] [] where f k us vs = (xs ++ ys) : f (k+1) xs ys where xs = us ++ qs ys = sortBy (compare `on` snd . properFraction . sqrt . fromIntegral) (vs ++ rs) (qs, rs) = span ((== 1) . a010052') [k*(k+2)+1 .. (k+1)*(k+3)] -- Reinhard Zumkeller, Apr 22 2015 -
Mathematica
row[n_] := SortBy[Range[n(n+2)], If[IntegerQ[Sqrt[#]], 0, N[FractionalPart[ Sqrt[#]]]]&]; Array[row, 5] // Flatten (* Jean-François Alcover, Sep 17 2019 *)
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PARI
arow(n)=vecsort(vector(n*(n+2),k,if(issquare(k),0.,sqrt(k)-floor(sqrt(k)))),,1) \\ This relies on vecsort being stable.
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