cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A261585 Number of sexagesimal digits of Fibonacci numbers in base-60 representation.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10
Offset: 0

Views

Author

Reinhard Zumkeller, Sep 09 2015

Keywords

Comments

a(n) = length of n-th row in table A261575.
a(n)/n tends towards log_60(phi) = 0.117530856953191562796405213751... - Hans J. H. Tuenter, Jul 13 2025

Links

Crossrefs

Cf. A261575, A000045, A001622, A060384.

Programs

  • Haskell
    a261585 = length . a261575_row
  • Mathematica
    Join[{1}, IntegerLength[Fibonacci[Range[100]], 60]] (* Paolo Xausa, Feb 19 2024 *)

Formula

For n>1, a(n) = 1+floor(n*log_60(phi)-log_60(5)/2), where phi=(1+sqrt(5))/2, the golden ratio. - Hans J. H. Tuenter, Jul 13 2025.

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

Views

Author

Reinhard Zumkeller, Sep 09 2015

Keywords

Comments

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

Links

Crossrefs

Cf. A261575, A000045, A004090, A261598.

Programs

  • Haskell
    a261587 = sum . a261575_row
  • Maple
    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
  • Mathematica
    Table[Total[IntegerDigits[n,60]],{n,Fibonacci[Range[0,60]]}] (* Harvey P. Dale, Aug 02 2019 *)
  • PARI
    a(n) = sumdigits(fibonacci(n), 60); \\ Michel Marcus, Jan 22 2022

A261598 Product 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, 29, 48, 159, 102, 100, 432, 962, 172, 369, 2340, 156, 2420, 14763, 29952, 25000, 18447, 67716, 22848, 63800, 21420, 217854, 2250, 35264, 34944, 99330, 14364, 1300500, 0, 8726016, 2303910, 544272, 9728000, 5615610, 8419950
Offset: 0

Views

Author

Reinhard Zumkeller, Sep 09 2015

Keywords

Comments

a(n) is the product of the terms in the n-th row of table A261575.
Conjecture: a(n) = 0 for n > 3329 (empirically checked up to 36000).

Links

Crossrefs

Cf. A261575, A000045, A246558, A261587.

Programs

  • Haskell
    a261598 = product . a261575_row
  • Maple
    a:= n-> mul(i, i=convert((<<0|1>, <1|1>>^n)[1, 2], base, 60)):
seq(a(n), n=0..44);  # Alois P. Heinz, Jan 22 2022
  • Mathematica
    Apply[Times, IntegerDigits[Fibonacci[Range[0, 50]], 60], {1}] (* Paolo Xausa, Feb 19 2024 *)
  • PARI
    a(n) = if (n, vecprod(digits(fibonacci(n), 60)), 0); \\ Michel Marcus, Jan 22 2022

A261606 a(n) = Fibonacci(n) mod 60.

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 29, 24, 53, 17, 10, 27, 37, 4, 41, 45, 26, 11, 37, 48, 25, 13, 38, 51, 29, 20, 49, 9, 58, 7, 5, 12, 17, 29, 46, 15, 1, 16, 17, 33, 50, 23, 13, 36, 49, 25, 14, 39, 53, 32, 25, 57, 22, 19, 41, 0, 41, 41, 22, 3, 25, 28, 53
Offset: 0

Views

Author

Reinhard Zumkeller, Sep 09 2015

Keywords

Comments

a(n) = A261575(n,0).
Periodic with period length 120. - Ray Chandler, Sep 23 2015

Links

Crossrefs

Cf. A000045, A261575, A261607, A003893.

Programs

  • Haskell
    a261606 n = a261606_list !! n
a261606_list = 0 : 1 : map (flip mod 60)
                           (zipWith (+) a261606_list $ tail a261606_list)
  • Mathematica
    Mod[Fibonacci[Range[67]], 60] (* Michael De Vlieger, Jan 22 2022 *)
  • PARI
    a(n) = fibonacci(n) % 60; \\ Michel Marcus, Jan 22 2022

Formula

a(0) = 0, a(1) = 1 and for n > 1: a(n) = (a(n-1) + a(n-2)) mod 60.

A261607 Initial digit of Fibonacci number F(n) in base 60.

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 1, 2, 3, 6, 10, 16, 26, 43, 1, 1, 3, 4, 7, 12, 20, 33, 54, 1, 2, 3, 6, 10, 16, 26, 42, 1, 1, 3, 4, 7, 12, 20, 33, 54, 1, 2, 3, 6, 10, 16, 26, 42, 1, 1, 2, 4, 7, 12, 20, 33, 53, 1, 2, 3, 6, 9, 16, 25, 42, 1, 1, 2, 4, 7, 12
Offset: 0

Views

Author

Reinhard Zumkeller, Sep 09 2015

Keywords

Links

Crossrefs

Cf. A000045, A261575, A261585, A261606, A008963, A001622.

Programs

  • Haskell
    a261607 = last . a261575_row
  • Mathematica
    IntegerDigits[Fibonacci[Range[0, 75]], 60][[All, 1]] (* Michael De Vlieger, Jan 22 2022 *)
  • PARI
    a(n) = if (n, digits(fibonacci(n), 60)[1], 0); \\ Michel Marcus, Jan 22 2022

Formula

a(n) = A261575(n, A261585(n)-1).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{d=1..59} d*log(1+1/d)/log(60) = 13.92958... . - Amiram Eldar, Jan 12 2023
For n>9, a(n) = floor(60^{alpha*n-beta}), where alpha=log_60(phi), beta=log_60(5)/2, {x}=x-floor(x) denotes the fractional part of x, and phi = (1+sqrt(5))/2 = A001622. - Hans J. H. Tuenter, Aug 26 2025
Showing 1-5 of 5 results.

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