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%I #12 Feb 19 2024 03:40:57
%S 0,1,1,2,3,5,8,13,21,34,55,29,1,24,2,53,3,17,6,10,10,27,16,37,26,4,43,
%T 41,9,1,45,52,1,26,2,3,11,55,4,37,57,7,48,52,12,25,50,20,13,43,33,38,
%U 33,54,51,16,28,1,29,50,22,2,20,7,51,3,49,57,13,6
%N Table of Fibonacci numbers in base-60 representation: row n contains the sexagesimal digits of A000045(n) in reversed order.
%C A261585(n) = length of n-th row;
%C T(n,0) = A261606(n) = in base 60: last sexagesimal digit of A000045(n);
%C T(n,A261607(n)-1) = A261607(n) = in base 60: initial sexagesimal digit of A000045(n);
%C A000045(n) = sum(T(n,k)*60^k : k = 0..A261585(n)-1).
%H Reinhard Zumkeller, <a href="/A261575/b261575.txt">Rows n = 0..1000 of triangle, flattened</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Sexagesimal.html">Sexagesimal</a>
%H Wikipedia, <a href="http://www.wikipedia.org/wiki/Sexagesimal">Sexagesimal</a>
%e A000045(42) = 20*60^4 + 40*60^3 + 20*60^2 + 38*60^1 + 16*60^0 = 267914296.
%e . ----------------------------------------------------------------------
%e . n | T(n,*) n | T(n,*) n | T(n,*)
%e . ----+--------- ----+--------------- ----+-------------------------
%e . 0 | [0] 21 | [26,2,3] 42 | [16,38,20,40,20]
%e . 1 | [1] 22 | [11,55,4] 43 | [17,7,55,26,33]
%e . 2 | [1] 23 | [37,57,7] 44 | [33,45,15,7,54]
%e . 3 | [2] 24 | [48,52,12] 45 | [50,52,10,34,27,1]
%e . 4 | [3] 25 | [25,50,20] 46 | [23,38,26,41,21,2]
%e . 5 | [5] 26 | [13,43,33] 47 | [13,31,37,15,49,3]
%e . 6 | [8] 27 | [38,33,54] 48 | [36,9,4,57,10,6]
%e . 7 | [13] 28 | [51,16,28,1] 49 | [49,40,41,12,0,10]
%e . 8 | [21] 29 | [29,50,22,2] 50 | [25,50,45,9,11,16]
%e . 9 | [34] 30 | [20,7,51,3] 51 | [14,31,27,22,11,26]
%e . 10 | [55] 31 | [49,57,13,6] 52 | [39,21,13,32,22,42]
%e . 11 | [29,1] 32 | [9,5,5,10] 53 | [53,52,40,54,33,8,1]
%e . 12 | [24,2] 33 | [58,2,19,16] 54 | [32,14,54,26,56,50,1]
%e . 13 | [53,3] 34 | [7,8,24,26] 55 | [25,7,35,21,30,59,2]
%e . 14 | [17,6] 35 | [5,11,43,42] 56 | [57,21,29,48,26,50,4]
%e . 15 | [10,10] 36 | [12,19,7,9,1] 57 | [22,29,4,10,57,49,7]
%e . 16 | [27,16] 37 | [17,30,50,51,1] 58 | [19,51,33,58,23,40,12]
%e . 17 | [37,26] 38 | [29,49,57,0,3] 59 | [41,20,38,8,21,30,20]
%e . 18 | [4,43] 39 | [46,19,48,52,4] 60 | [0,12,12,7,45,10,33]
%e . 19 | [41,9,1] 40 | [15,9,46,53,7] 61 | [41,32,50,15,6,41,53]
%e . 20 | [45,52,1] 41 | [1,29,34,46,12] 62 | [41,44,2,23,51,51,26,1]
%t Reverse[IntegerDigits[Fibonacci[Range[0, 50]], 60], 2] (* _Paolo Xausa_, Feb 19 2024 *)
%o (Haskell)
%o a261575 n k = a261575_tabf !! n !! k
%o a261575_row n = a261575_tabf !! n
%o a261575_tabf = [0] : [1] :
%o zipWith (add 0) (tail a261575_tabf) a261575_tabf where
%o add c (a:as) (b:bs) = y : add c' as bs where (c', y) = divMod (a+b+c) 60
%o add c (a:as) [] = y : add c' as [] where (c', y) = divMod (a+c) 60
%o add 1 _ _ = [1]
%o add _ _ _ = []
%Y Cf. A000045, A261585 (row lengths), A261587 (row sums), A261598 (row products), A261606 (left edge), A261607 (right edge).
%K nonn,tabf,base
%O 0,4
%A _Reinhard Zumkeller_, Sep 09 2015
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