Template:Sequence of the Day for July 31

Intended for: July 31, 2012

Timetable

• First draft entered by Alonso del Arte on April 30, 2011 ✓
• Draft reviewed by Daniel Forgues on May 6, 2011 ✓
• Draft approved by Alonso del Arte on July 28, 2011 ✓

Yesterday's SOTD * Tomorrow's SOTD

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A173419: Length of shortest computation yielding

n, n   ≥   1,

using addition, subtraction and multiplication.

{ 0, 1, 2, 2, 3, 3, 4, 3, 3, 4, 4, 4, 5, ... }

So you start with

x0 = 1, xm = n

and then through successive

xk = xi + xj

,

xk = xi xj

, or

xk = xi  −  xj

operations for some

0   ≤   i, j < k

, you get to

n

. The fun is of course getting there in as few steps as possible. Prime

n

are not necessarily more difficult to get to than their neighbors: 29, for example, requires five operations, just as 28 and 30 do.