A261598 -id:A261598 - cp's OEIS frontend

A246558 Product of the digits of the n-th Fibonacci number.

0, 1, 1, 2, 3, 5, 8, 3, 2, 12, 25, 72, 16, 18, 147, 0, 504, 315, 320, 32, 1260, 0, 49, 3360, 3456, 0, 162, 1728, 168, 720, 0, 7776, 0, 33600, 0, 30240, 0, 15680, 0, 311040, 0, 0, 326592, 435456, 0, 0, 0, 0, 0, 0, 0, 0, 0, 102060, 3951360, 24883200, 1411200

Offset: 0

Indrani Das, Nov 12 2014

a(n) > 0 iff n in A076564.

Probably, the last nonzero term is a(184). - Giovanni Resta, Jul 14 2015

			Fibonacci(7) = 13, thus a(7) = 1*3 = 3.

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Cf. A000045, A004090, A076564.
Cf. A007954, A259773.
Cf. A261598.

a246558 = a007954 . a000045 -- Reinhard Zumkeller, Nov 17 2014

[0] cat [&*Intseq(Fibonacci(n)): n in [1..100]]; // Vincenzo Librandi, Jan 04 2020

Array[Times@@IntegerDigits@Fibonacci[#]&, 100, 0] (* Vincenzo Librandi, Jan 04 2020 *)

a(n) = if (n, vecprod(digits(fibonacci(n))), 0); \\ Michel Marcus, Feb 11 2025

a(n) = A007954(A000045(n)). - Reinhard Zumkeller, Nov 17 2014

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

Original entry on oeis.org

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

Reinhard Zumkeller, Sep 09 2015

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).

			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]

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

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

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   _ = []

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

A261587 Sum of sexagesimal digits of Fibonacci numbers in base-60 representation.

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 30, 26, 56, 23, 20, 43, 63, 47, 51, 98, 31, 70, 101, 112, 95, 89, 125, 96, 103, 81, 125, 29, 95, 65, 101, 48, 149, 138, 169, 130, 122, 134, 138, 154, 174, 151, 148, 122, 152, 156, 131, 169, 241, 233, 179, 235, 178, 236

Offset: 0

Reinhard Zumkeller, Sep 09 2015

a(n) is the sum of the n-th row of table A261575.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Sexagesimal
Wikipedia, Sexagesimal

Cf. A261575, A000045, A004090, A261598.

Haskell
```
a261587 = sum . a261575_row
```

a:= n-> add(i, i=convert((<<0|1>, <1|1>>^n)[1, 2], base, 60)):
seq(a(n), n=0..60);  # Alois P. Heinz, Jan 22 2022

Table[Total[IntegerDigits[n,60]],{n,Fibonacci[Range[0,60]]}] (* Harvey P. Dale, Aug 02 2019 *)

a(n) = sumdigits(fibonacci(n), 60); \\ Michel Marcus, Jan 22 2022

cp's OEIS Frontend

A246558 Product of the digits of the n-th Fibonacci number.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Magma

Mathematica

PARI

Formula

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Mathematica

A261587 Sum of sexagesimal digits of Fibonacci numbers in base-60 representation.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI