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A261575 Table of Fibonacci numbers in base-60 representation: row n contains the sexagesimal digits of A000045(n) in reversed order.

%I A261575 #13 Feb 16 2025 08:33:26
%S A261575 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 A261575 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 A261575 33,54,51,16,28,1,29,50,22,2,20,7,51,3,49,57,13,6
%N A261575 Table of Fibonacci numbers in base-60 representation: row n contains the sexagesimal digits of A000045(n) in reversed order.
%C A261575 A261585(n) = length of n-th row;
%C A261575 T(n,0) = A261606(n) = in base 60: last sexagesimal digit of A000045(n);
%C A261575 T(n,A261607(n)-1) = A261607(n) = in base 60: initial  sexagesimal digit of A000045(n);
%C A261575 A000045(n) = sum(T(n,k)*60^k : k = 0..A261585(n)-1).
%H A261575 Reinhard Zumkeller, <a href="/A261575/b261575.txt">Rows n = 0..1000 of triangle, flattened</a>
%H A261575 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Sexagesimal.html">Sexagesimal</a>
%H A261575 Wikipedia, <a href="http://www.wikipedia.org/wiki/Sexagesimal">Sexagesimal</a>
%e A261575 A000045(42) = 20*60^4 + 40*60^3 + 20*60^2 + 38*60^1 + 16*60^0 = 267914296.
%e A261575 . ----------------------------------------------------------------------
%e A261575 .   n | T(n,*)       n | T(n,*)             n | T(n,*)
%e A261575 . ----+---------   ----+---------------   ----+-------------------------
%e A261575 .   0 | [0]         21 | [26,2,3]          42 | [16,38,20,40,20]
%e A261575 .   1 | [1]         22 | [11,55,4]         43 | [17,7,55,26,33]
%e A261575 .   2 | [1]         23 | [37,57,7]         44 | [33,45,15,7,54]
%e A261575 .   3 | [2]         24 | [48,52,12]        45 | [50,52,10,34,27,1]
%e A261575 .   4 | [3]         25 | [25,50,20]        46 | [23,38,26,41,21,2]
%e A261575 .   5 | [5]         26 | [13,43,33]        47 | [13,31,37,15,49,3]
%e A261575 .   6 | [8]         27 | [38,33,54]        48 | [36,9,4,57,10,6]
%e A261575 .   7 | [13]        28 | [51,16,28,1]      49 | [49,40,41,12,0,10]
%e A261575 .   8 | [21]        29 | [29,50,22,2]      50 | [25,50,45,9,11,16]
%e A261575 .   9 | [34]        30 | [20,7,51,3]       51 | [14,31,27,22,11,26]
%e A261575 .  10 | [55]        31 | [49,57,13,6]      52 | [39,21,13,32,22,42]
%e A261575 .  11 | [29,1]      32 | [9,5,5,10]        53 | [53,52,40,54,33,8,1]
%e A261575 .  12 | [24,2]      33 | [58,2,19,16]      54 | [32,14,54,26,56,50,1]
%e A261575 .  13 | [53,3]      34 | [7,8,24,26]       55 | [25,7,35,21,30,59,2]
%e A261575 .  14 | [17,6]      35 | [5,11,43,42]      56 | [57,21,29,48,26,50,4]
%e A261575 .  15 | [10,10]     36 | [12,19,7,9,1]     57 | [22,29,4,10,57,49,7]
%e A261575 .  16 | [27,16]     37 | [17,30,50,51,1]   58 | [19,51,33,58,23,40,12]
%e A261575 .  17 | [37,26]     38 | [29,49,57,0,3]    59 | [41,20,38,8,21,30,20]
%e A261575 .  18 | [4,43]      39 | [46,19,48,52,4]   60 | [0,12,12,7,45,10,33]
%e A261575 .  19 | [41,9,1]    40 | [15,9,46,53,7]    61 | [41,32,50,15,6,41,53]
%e A261575 .  20 | [45,52,1]   41 | [1,29,34,46,12]   62 | [41,44,2,23,51,51,26,1]
%t A261575 Reverse[IntegerDigits[Fibonacci[Range[0, 50]], 60], 2] (* _Paolo Xausa_, Feb 19 2024 *)
%o A261575 (Haskell)
%o A261575 a261575 n k = a261575_tabf !! n !! k
%o A261575 a261575_row n = a261575_tabf !! n
%o A261575 a261575_tabf = [0] : [1] :
%o A261575    zipWith (add 0) (tail a261575_tabf) a261575_tabf where
%o A261575    add c (a:as) (b:bs) = y : add c' as bs where (c', y) = divMod (a+b+c) 60
%o A261575    add c (a:as) [] = y : add c' as [] where (c', y) = divMod (a+c) 60
%o A261575    add 1 _ _ = [1]
%o A261575    add _ _ _ = []
%Y A261575 Cf. A000045, A261585 (row lengths), A261587 (row sums), A261598 (row products), A261606 (left edge), A261607 (right edge).
%K A261575 nonn,tabf,base
%O A261575 0,4
%A A261575 _Reinhard Zumkeller_, Sep 09 2015