A372050 The index of the largest Fibonacci number that divides the sum of Fibonacci numbers with indices 1 through A000217(n) (the n-th triangular number).

2, 3, 5, 7, 8, 12, 14, 18, 24, 28, 35, 41, 46, 54, 60, 68, 78, 89, 97, 107, 116, 128, 138, 150, 164, 176, 191, 205, 218, 234, 248, 264, 282, 298, 317, 335, 352, 372, 390, 410, 432, 452, 475, 497, 518, 542, 564, 588, 614, 638, 665, 691, 716, 744, 770, 798, 828, 856, 887, 917, 946, 978

Offset: 1

Author

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

Keywords

• nonn

Comments

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

Examples

			For example, the sum of the first ten Fibonacci numbers is 143. The largest Fibonacci that divides this sum is 13, the seventh Fibonacci number. Thus, as 10 is the fourth triangular number a(4) = 7. After the division we get 143/13 = 11, the fifth Lucas number.
		

Crossrefs

Cf. A000032, A000045, A000071, A000217, A054494, A075850, A372048, A372049, A372051.