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

0,4

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).

Links

Reinhard Zumkeller, Rows n = 0..1000 of triangle, flattened

Eric Weisstein's World of Mathematics, Sexagesimal

Wikipedia, Sexagesimal

Example

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]

Mathematica

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

Prog

(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 _ _ _ = []

Crossrefs

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

Sequence in context: A147660 A013987 A261607 * A261606 A261598 A261587

Adjacent sequences: A261572 A261573 A261574 * A261576 A261577 A261578

Keyword

nonn,tabf,base

Author

Reinhard Zumkeller, Sep 09 2015

Status

approved