A372049 - OEIS

A372049

a(n) is the index of the Lucas number that is the ratio of the sum of the first n Fibonacci numbers divided by the largest possible Fibonacci number.

1, 1, 0, 4, 3, 3, 5, 6, 5, 5, 7, 8, 7, 7, 9, 10, 9, 9, 11, 12, 11, 11, 13, 14, 13, 13, 15, 16, 15, 15, 17, 18, 17, 17, 19, 20, 19, 19, 21, 22, 21, 21, 23, 24, 23, 23, 25, 26, 25, 25, 27, 28, 27, 27, 29, 30, 29, 29, 31, 32, 31, 31, 33, 34, 33, 33, 35, 36, 35, 35, 37, 38, 37, 37, 39, 40, 39, 39, 41, 42, 41

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OFFSET

1,4

COMMENTS

The sum of the first n Fibonacci numbers is sequence A000071.

When we divide the sum by the largest Fibonacci number that divides the sum, we always get a Lucas number.

For n > 3, a(n+4) = a(n)+2.

LINKS

Table of n, a(n) for n=1..81.

Tanya Khovanova and the MIT PRIMES STEP senior group, Fibonacci Partial Sums Tricks, arXiv:2409.01296 [math.HO], 2024.

EXAMPLE

The sum of the first ten Fibonacci numbers is 143. The largest Fibonacci that divides this sum is 13, the seventh Fibonacci number. After the division we get 143/13 = 11, the fifth Lucas number. Thus, a(10) = 5.

CROSSREFS

Cf. A000032, A000045, A000071, A372048.

Sequence in context: A362123 A052360 A263046 * A154913 A154915 A238376

Adjacent sequences: A372046 A372047 A372048 * A372050 A372051 A372052

KEYWORD

nonn

AUTHOR

Tanya Khovanova and MIT PRIMES senior group, Apr 17 2024

STATUS

approved