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

Author

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

Keywords

• nonn

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.

Examples

			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.