Template:Sequence of the Day for April 20

Intended for: April 20, 2013

Timetable

• First draft entered by Alonso del Arte on March 17, 2012 ✓
• Draft reviewed by Daniel Forgues on April 15, 2016 ✓
• Draft to be approved by March 20, 2013

Yesterday's SOTD * Tomorrow's SOTD

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A plot of digit sums of Fibonacci numbers. The red line is

y = (c  −  1) x

, where

c = 9 20 log10 φ

.

A020995: Numbers

n

such that sum of digits of

Fn

is

n

.

{ 0, 1, 5, 10, 31, 35, 62, 72, 175, 180, 216, 251, 252, 360, 494, 504, 540, 946, 1188, 2222, ¿ ... ? }

The 180^th Fibonacci number is 18547707689471986212190138521399707760, and

1 + 8 + 5 + 4 + 7 + 7 + 0 + 7 + 6 + 8 + 9 + 4 + 7 + 1 + 9 + 8 + 6 + 2 + 1 + 2 + 1 + 9 + 0 + 1 + 3 + 8 + 5 + 2 + 1 + 3 + 9 + 9 + 7 + 0 + 7 + 7 + 6 + 0 = 180.

Is this sequence finite? There are conflicting opinions on the matter. And even if it is finite, that does not guarantee that 2222 is the final term. The following graph by Robert Israel, suggested by David Wilson, suggests the sequence is finite.