A372051 a(n) is the index of the Lucas number that is a ratio of the sum of the first A000217(n) Fibonacci numbers divided by the largest possible Fibonacci number.

1, 0, 3, 5, 9, 11, 16, 20, 23, 29, 33, 39, 47, 53, 62, 70, 77, 87, 95, 105, 117, 127, 140, 152, 163, 177, 189, 203, 219, 233, 250, 266, 281, 299, 315, 333, 353, 371, 392, 412, 431, 453, 473, 495, 519, 541, 566, 590, 613, 639, 663, 689, 717, 743, 772, 800, 827, 857, 885, 915, 947, 977, 1010, 1042

Offset

1,3

Comments

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

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

A000217() are the triangular numbers.

Links

Table of n, a(n) for n=1..64.

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, as 10 is the fourth triangular number, a(4) = 5.

Crossrefs

Cf. A000032, A000045, A000071, A000217, A372048, A372049, A372050.

Sequence in context: A024414 A072391 A310038 * A036696 A111039 A114512

Adjacent sequences: A372048 A372049 A372050 * A372052 A372053 A372054

Keyword

nonn

Author

Tanya Khovanova and MIT PRIMES STEP junior group, Apr 17 2024

Status

approved