# What is a Recursive Word™?

In the spirit of the What is a Word™/Phrase™ series started by JLee, a special brand of Phrase™ and Word™ puzzles.

If a word conforms to a special rule, I call it a Recursive Word™.
Use the examples below to find the rule.

$$% set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{0.0}} \def\Title{\textbf{ Recursive }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\ \def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Words }^™\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2017.02.04}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{ SURVIVOR }&\text{ SHIPWRECK }\\ \hline \text{ AGE }&\text{ YEAR }\\ \hline \text{ MALARIA }&\text{ AFRICA }\\ \hline \text{ FOREVER }&\text{ ETERNITY }\\ \hline \text{ AUGUST }&\text{ JULY }\\ \hline \text{ AGILE }&\text{ SLOW }\\ \hline \text{ ONE }&\text{ ZERO }\\ \hline \text{ SEQUENCE }&\text{ SERIES }\\ \hline \text{ KEBAB }&\text{ SANDWICH }\\ \hline \text{ SKY }&\text{ SEA }\\ \hline \text{ PIANO }&\text{ GUITAR }\\ \hline \text{ DECEMBER }&\text{ NOVEMBER }\\ \hline \text{ ANOMALIES }&\text{ ANOMALY }\\ \hline \end{array}$$

The CSV version:

Recursive Words™,Not Recursive Words™
SURVIVOR, SHIPWRECK
AGE, YEAR
MALARIA, AFRICA
FOREVER, ETERNITY
AUGUST, JULY
AGILE, SLOW
ONE, ZERO
SEQUENCE, SERIES
KEBAB, SANDWICH
SKY, SEA
PIANO, GUITAR
DECEMBER, NOVEMBER
ANOMALIES, ANOMALY


These are not the only examples of Recursive Words™; many more exist.

What is the special rule these words conform to?

Hint 1:

I would have called them Golden Words™, but they exist already.

• Just to confirm, does this puzzle follow the rule: "The puzzle satisfies the series' inbuilt assumption, that each word can be tested for whether it is a Recursive Word™ without relying on the other words." – David Foong Aug 11 '17 at 15:24
• Hmm...Every Recursive word has letters that can be removed to make a totally unrelated word. But a few of the non-recursive words have this property as well. – Morgan G Aug 11 '17 at 16:35
• @MorganG What about SKY? – David Foong Aug 11 '17 at 17:18
• SK is the abbreviation for the Canadian province Saskatchewan... ;) Nah, it doesn't really fit, you're right. – Morgan G Aug 11 '17 at 17:25
• There's no H, J, W, X, Z in recursive while in other Q, V, X, Z are missing. – Nikhil Bhavar Aug 13 '17 at 3:52

A recursive word is simply:

A word whose letters add up to a number in the Fibonacci sequence. (1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233...) A Not Recursive Word™'s letters do not add up to one of these numbers

For example...

SURVIVOR: 19 + 21 + 18 +22 + 9 + 22 + 15 + 18 = 144
FOREVER: 6 + 15 + 18 + 5 + 22 + 5 + 18 = 89
ONE: 15 + 14 + 5 = 34
SKY: 19 + 11 + 25 = 55
AGE: 1 + 7 + 5 = 13

Hint 1 would be more appropriate because...

The Fibonacci sequence's growth is very similar to the Golden Ratio

It is called a Recursive Word™ because:

the Fibonnacci sequence can be defined as a recursive function, meaning a function that calls itself in itself.

However...

The Fibonnacci sequence can be adequatetly defined without recursion, so I'm not sure Recursive Word™ is the best defintion for these words! Golden Word™ would indeed be better.

I wonder what the longest Recursive Word™ is?

• incomprehensibilities has 21 letters and a letter score of 233. – w l Aug 14 '17 at 15:05
• Chemistry to the rescue: "hydroxydehydrocorticosterone" has 28 letters and a score of 377. :) – M Oehm Aug 14 '17 at 16:13
• @MOehm My dictionary had that as well, but it being a name and having the ability to create arbitrary long words for molecules made me dismiss it. – w l Aug 15 '17 at 7:32
• @wl: That's the drawback of such questions: You just run a search on a dictionary. It makes them boring to solve, although the search might yield some interesting results. (By the way, "incomprehensibilities" looks a bit artificial to me, too, as a plural of something that probably is a mass noun.) – M Oehm Aug 15 '17 at 9:24