A031121 -id:A031121 - cp's OEIS frontend

A336526 a(n) is the least k > 1 such that A031121(n) = F(k*m)/F(m) for some m.

2, 3, 2, 2, 5, 2, 3, 2, 7, 3, 2, 4, 2, 9, 2, 3, 5, 4, 2, 11, 3, 2, 6, 2, 13, 5, 2, 3, 4, 7, 2, 15, 3, 2, 8, 6, 4, 2, 17, 2, 3, 5, 9, 2, 19, 7, 3, 2, 4, 10, 2, 21, 5, 2, 3, 6, 11, 8, 4, 2, 23, 3, 2, 12, 2, 25, 9, 2, 3, 4, 5, 7, 13, 6, 2, 27, 3, 2

Offset: 1

M. Farrokhi D. G., Jul 25 2020

M. Farrokhi D. G., Table of n, a(n) for n = 1..999
M. Farrokhi D. G., Some remarks on the equation F_n=kF_m in Fibonacci numbers, J. Integer Seq. 10 (2007), no. 5, Article 07.5.7, 9 pp.

Cf. A000045, A031121, A031122.

A031122 Integers that appear as ratios of Fibonacci numbers F(kn)/F(k), but omitting Fibonacci numbers F(n)/F(1) and Lucas numbers F(2n)/F(n).

Original entry on oeis.org

17, 48, 72, 122, 305, 323, 329, 842, 1292, 1353, 2208, 2255, 5473, 5777, 5796, 15005, 15128, 15456, 23184, 24447, 39602, 98209, 103683, 103729, 104005, 105937, 166408, 271442, 416020, 439128, 709805, 710648, 726103, 1762289

Offset: 1

Dan Hoey

T. D. Noe, Table of n, a(n) for n=1..1000

Cf. A031121.

a031122(mk,mn,x) = local(v,vv,j,i); v=[]; for(k=3,mk, for(n=3,mn,v=concat(v,[fibonacci(k*n)/fibonacci(k)]))); v=vecsort(v); vv=[v[1]]; for(j=2,matsize(v)[2], if(v[j-1]Klaus Brockhaus, Oct 20 2001

Corrected and extended by Don Reble, Oct 20 2001

A333357 Integers that cannot be expressed as the ratio of 2 Fibonacci numbers.

Original entry on oeis.org

6, 9, 10, 12, 14, 15, 16, 19, 20, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 77, 78, 79, 80

Offset: 1

M. Farrokhi D. G., Jul 24 2020

Any product of m > 1 Fibonacci numbers > 1 belongs to the sequence except for 4, 18, 48, and 72.

M. Farrokhi D. G., Table of n, a(n) for n = 1..10000
M. Farrokhi D. G., Some remarks on the equation F_n=kF_m in Fibonacci numbers, J. Integer Seq. 10 (2007), no. 5, Article 07.5.7, 9 pp.

Cf. A000045.

Complement of A031121.

l := Filtered(Set(List(Cartesian([1..21], [1..21]), x -> Fibonacci(x[1] * x[2])/Fibonacci(x[1]))), x -> x < 10000);;
Filtered([1..10000], x ->  not x in l);

cp's OEIS Frontend

A336526 a(n) is the least k > 1 such that A031121(n) = F(k*m)/F(m) for some m.

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A031122 Integers that appear as ratios of Fibonacci numbers F(kn)/F(k), but omitting Fibonacci numbers F(n)/F(1) and Lucas numbers F(2n)/F(n).

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A333357 Integers that cannot be expressed as the ratio of 2 Fibonacci numbers.

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