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

1,1

Comments

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

Links

Table of n, a(n) for n=1..62.

Example

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.

Sequence in context: A291485 A228898 A352695 * A076386 A177801 A073301

Adjacent sequences: A372047 A372048 A372049 * A372051 A372052 A372053

Keyword

nonn

Author

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

Status

approved