Template:Sequence of the Day for February 24

Intended for: February 24, 2012

Timetable

• First draft entered by Alonso del Arte on November 24, 2011 based on remarks by Eric Angelini and Neil Sloane ✓
• Draft reviewed by Daniel Forgues on February 22, 2016, February 24, 2017 ✓
• Draft to be approved by January 24, 2012

Yesterday's SOTD * Tomorrow's SOTD

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A109671:

a (1) = 1

; thereafter, for

k   ≥   1

,

a (2 k) = a (k)

, and

a (2 k + 1)

is the smallest positive number such that

| a (2 k  +  1)  −  a (2 k  −  1) | = a (k)

.

{ 1, 1, 2, 1, 1, 2, 3, 1, 2, 1, 1, 2, 3, 3, 6, 1, 5, ... }

This is a variant of the semi-Fibonacci numbers (A030067). The sequence is self-describing: the sequence of the absolute differences between odd-indexed terms is the sequence itself. It appears that the record values form sequence A038754 and occur at indices of the form

2 k  −  1

. It remains an open question whether or not the sequence contains every positive integer (see A169741).