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

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, 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, 33, 54, 51, 16, 28, 1, 29, 50, 22, 2, 20, 7, 51, 3, 49, 57, 13, 6

Offset: 0

Author

Reinhard Zumkeller, Sep 09 2015

Keywords

• nonn
• tabf
• base

Comments

A261585(n) = length of n-th row;

T(n,0) = A261606(n) = in base 60: last sexagesimal digit of A000045(n);

T(n,A261607(n)-1) = A261607(n) = in base 60: initial sexagesimal digit of A000045(n);

A000045(n) = sum(T(n,k)*60^k : k = 0..A261585(n)-1).

Examples

			A000045(42) = 20*60^4 + 40*60^3 + 20*60^2 + 38*60^1 + 16*60^0 = 267914296.
. ----------------------------------------------------------------------
.   n | T(n,*)       n | T(n,*)             n | T(n,*)
. ----+---------   ----+---------------   ----+-------------------------
.   0 | [0]         21 | [26,2,3]          42 | [16,38,20,40,20]
.   1 | [1]         22 | [11,55,4]         43 | [17,7,55,26,33]
.   2 | [1]         23 | [37,57,7]         44 | [33,45,15,7,54]
.   3 | [2]         24 | [48,52,12]        45 | [50,52,10,34,27,1]
.   4 | [3]         25 | [25,50,20]        46 | [23,38,26,41,21,2]
.   5 | [5]         26 | [13,43,33]        47 | [13,31,37,15,49,3]
.   6 | [8]         27 | [38,33,54]        48 | [36,9,4,57,10,6]
.   7 | [13]        28 | [51,16,28,1]      49 | [49,40,41,12,0,10]
.   8 | [21]        29 | [29,50,22,2]      50 | [25,50,45,9,11,16]
.   9 | [34]        30 | [20,7,51,3]       51 | [14,31,27,22,11,26]
.  10 | [55]        31 | [49,57,13,6]      52 | [39,21,13,32,22,42]
.  11 | [29,1]      32 | [9,5,5,10]        53 | [53,52,40,54,33,8,1]
.  12 | [24,2]      33 | [58,2,19,16]      54 | [32,14,54,26,56,50,1]
.  13 | [53,3]      34 | [7,8,24,26]       55 | [25,7,35,21,30,59,2]
.  14 | [17,6]      35 | [5,11,43,42]      56 | [57,21,29,48,26,50,4]
.  15 | [10,10]     36 | [12,19,7,9,1]     57 | [22,29,4,10,57,49,7]
.  16 | [27,16]     37 | [17,30,50,51,1]   58 | [19,51,33,58,23,40,12]
.  17 | [37,26]     38 | [29,49,57,0,3]    59 | [41,20,38,8,21,30,20]
.  18 | [4,43]      39 | [46,19,48,52,4]   60 | [0,12,12,7,45,10,33]
.  19 | [41,9,1]    40 | [15,9,46,53,7]    61 | [41,32,50,15,6,41,53]
.  20 | [45,52,1]   41 | [1,29,34,46,12]   62 | [41,44,2,23,51,51,26,1]
		

Links

• Reinhard Zumkeller, Rows n = 0..1000 of triangle, flattened
• Eric Weisstein's World of Mathematics, Sexagesimal
• Wikipedia, Sexagesimal

Crossrefs

Cf. A000045, A261585 (row lengths), A261587 (row sums), A261598 (row products), A261606 (left edge), A261607 (right edge).

Programs

Haskell

a261575 n k = a261575_tabf !! n !! k
a261575_row n = a261575_tabf !! n
a261575_tabf = [0] : [1] :
   zipWith (add 0) (tail a261575_tabf) a261575_tabf where
   add c (a:as) (b:bs) = y : add c' as bs where (c', y) = divMod (a+b+c) 60
   add c (a:as) [] = y : add c' as [] where (c', y) = divMod (a+c) 60
   add 1   = [1]
   add   _ = []

Mathematica

Reverse[IntegerDigits[Fibonacci[Range[0, 50]], 60], 2] (* Paolo Xausa, Feb 19 2024 *)