A035105 -id:A035105 - cp's OEIS frontend

A190278 Number of decimal digits in LCM of Fibonacci sequence {F_1, ..., F_n}.

1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 15, 17, 20, 21, 25, 27, 29, 31, 36, 38, 42, 44, 48, 51, 56, 58, 64, 67, 72, 75, 80, 83, 90, 94, 99, 103, 111, 113, 122, 126, 131, 136, 145, 149, 157, 162, 168, 173, 184, 188, 196, 201, 209, 215

Offset: 1

Jonathan Vos Post, May 07 2011

Implicitly in Mathematics Teacher, Problem 15, pp. 684-685, May 2011.

			a(4) = 1 because lcm(F_1, F_2, F_3, F_4) = 6 has one decimal digit.
a(19) = 25 because lcm(F_1, ..., F_19) = 2679944489486672512824720 has 25 decimal digits.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A000045, A035105, A055642.

with(combinat):
b:= proc(n) option remember;
      `if`(n=1, 1, ilcm(b(n-1), fibonacci(n)))
    end:
a:= n-> length(b(n)):
seq(a(n), n=1..80); # Alois P. Heinz, Jul 28 2011

Table[IntegerLength[LCM@@Fibonacci[Range[n]]],{n,60}] (* Harvey P. Dale, Jan 10 2025 *)

a(n) = #Str(lcm(vector(n, k, fibonacci(k)))); \\ Michel Marcus, Mar 13 2018

a(n) = A055642(A035105(n)) = floor(log_10(10*A035105(n))).

A355322 LCM of Lucas numbers {L(1), L(2), ..., L(n)}.

Original entry on oeis.org

1, 3, 12, 84, 924, 2772, 80388, 3778236, 71786484, 2943245844, 585705922956, 13471236227988, 7018514074781748, 1972202455013671188, 61138276105423806828, 134932175364670341669396, 481842798227237790101413116, 154671538230943330622553610236

Offset: 1

Clark Kimberling, Jul 16 2022

Cf. A000032, A035105 (LCM of Fibonacci numbers), essentially the same as A062954.

Table[LCM @@ LucasL[Range[n]], {n, 1, 16}]
Module[{nn=20,ln},ln=LucasL[Range[nn]];Table[LCM@@Take[ln,n],{n,nn}]] (* Harvey P. Dale, Sep 26 2024 *)

Lucas(n) = real((2 + quadgen(5)) * quadgen(5)^n); \\ A000032
a(n) = lcm(apply(Lucas, [1..n])); \\ Michel Marcus, Jul 17 2022

from math import lcm
from sympy import lucas
def A355322(n): return lcm(*(lucas(i) for i in range(1,n+1))) # Chai Wah Wu, Jul 17 2022

A342875 Decimal expansion of 3*log(phi)/Pi^2, where phi is the golden ratio.

Original entry on oeis.org

1, 4, 6, 2, 7, 0, 8, 5, 5, 0, 9, 3, 1, 8, 5, 7, 9, 4, 3, 3, 7, 7, 3, 6, 9, 7, 0, 4, 9, 2, 6, 2, 3, 1, 5, 6, 2, 6, 5, 4, 6, 2, 3, 9, 7, 8, 1, 7, 3, 8, 3, 2, 3, 7, 3, 7, 5, 3, 6, 9, 8, 8, 4, 7, 1, 4, 4, 9, 9, 5, 6, 8, 2, 5, 8, 6, 4, 7, 8, 2, 6, 0, 3, 7, 2, 6, 7

Offset: 0

Stefano Spezia, Mar 28 2021

			0.1462708550931857943377369704926...

Yuri V. Matiyasevich and Richard K. Guy, A new formula for Pi, The American Mathematical Monthly, Vol 93, No. 8 (1986), pp. 631-635.
Carlo Sanna, On the least common multiple of shifted powers, arXiv:2103.07967 [math.NT], 2021.

Cf. A000796, A001622, A002388, A002390, A003266, A035105.

First[RealDigits[N[3Log[(1+Sqrt[5])/2]/Pi^2,87]]]

A374667 Triangle T(n,k) (1 <= k <= n) read by rows: T(n,k) = c_n * F(k)/F(k+2) where c_n = LCM of F(3), F(4), ... F(n+2) (and F() are the Fibonacci numbers).

Original entry on oeis.org

1, 3, 2, 15, 10, 12, 60, 40, 48, 45, 780, 520, 624, 585, 600, 5460, 3640, 4368, 4095, 4200, 4160, 92820, 61880, 74256, 69615, 71400, 70720, 70980, 1021020, 680680, 816816, 765765, 785400, 777920, 780780, 779688, 90870780, 60580520, 72696624, 68153085, 69900600, 69234880, 69489420, 69392232, 69429360

Offset: 1

J. Lowell, Jul 15 2024

			Triangle begins:
      1;
      3,     2;
     15,    10,    12;
     60,    40,    48,    45;
    780,   520,   624,   585,   600;
   5460,  3640,  4368,  4095,  4200,  4160;
  92820, 61880, 74256, 69615, 71400, 70720, 70980;
  ...
Fifth row is 780, 520, 624, 585, 600. These are 1/2, 1/3, 2/5, 3/8, 5/13 of c_5 = 1560.

Cf. A000045, A035105.

row(n)={my(m=lcm(vector(n,k,fibonacci(k+2)))); vector(n, k, fibonacci(k)*m/fibonacci(k+2))}

T(n,k) = A035105(n+2) * A000045(k) / A000045(k+2).

cp's OEIS Frontend

A190278 Number of decimal digits in LCM of Fibonacci sequence {F_1, ..., F_n}.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A355322 LCM of Lucas numbers {L(1), L(2), ..., L(n)}.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

Python

A342875 Decimal expansion of 3*log(phi)/Pi^2, where phi is the golden ratio.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

A374667 Triangle T(n,k) (1 <= k <= n) read by rows: T(n,k) = c_n * F(k)/F(k+2) where c_n = LCM of F(3), F(4), ... F(n+2) (and F() are the Fibonacci numbers).

Views

Author

Keywords

Examples

Crossrefs

Programs

PARI

Formula