A309979 Hash Parker numbers: Integers whose real 32nd root's first six nonzero digits (after the decimal point) rearranged in ascending order are equal to 234477.

4, 1191, 2340, 4915, 8101, 8703, 13937, 13952, 14029, 14041, 25111, 25127, 26062, 26203, 26324, 26479, 26490, 27934, 28077, 28195, 50506, 50536, 52216, 52359, 52892, 55703, 55957, 56030, 56059, 56075, 56178, 56244, 56566, 56577, 74747, 75877, 75952, 75996, 80752, 80764, 80765

Offset: 1

Author

Dan Dart, Aug 25 2019

Keywords

• nonn
• base

Examples

			4^(1/32) = 1.0442737824274138...
Rearranging 442737 in ascending order gives 234477.
1191^(1/32) = 1.2477346... -> 247734 -> 234477;
2340^(1/32) = 1.2743478... -> 274347 -> 234477.
		

Links

• Matt Parker's YouTube Video, The A4 Paper Puzzle

Programs

Haskell

import Data.List
hash :: Double -> Inthash = read . sort . take 6 . filter (/='0') . drop 1 . dropWhile (/='.') . show . (** 0.03125)
main :: IO ()main = print $ map (floor . fst) . filter ((==234477) . snd) $ map (\x -> (x, hash x)) [2..1000000]

Mathematica

Select[Range[81000],With[{c=RealDigits[Surd[#,32],10,20]/.(0->Nothing)},Sort[Take[Drop[c[[1]],c[[2]]],6]]=={2,3,4,4,7,7}]&]//Quiet (* Harvey P. Dale, Jun 22 2025 *)