Here is an interesting sequence generated by a hidden connection to Fibonacci based on the letter-number association shown in Table 1:
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Table 1: source |
The sequence is OEIS A129938:
A129938: "Self-Fibonacci"; a(n) is the sum of the last nine terms. Sequence starts with 6, 9, 2, 15, 14, 1, 3, 3, 9 which are f, i, b, o, n, a, c, c, i if you consider a=1, b=2, c=3, ..., z=26.
The sequence begins 6, 9, 2, 15, 14, 1, 3, 3, 9, 62, 118, 227, 452, 889, 1764, 3527, 7051, 14099, 28189, ...
I only chanced upon this sequence because 28189, my diurnal age today, is a member. I've written about the various connections between numbers and letters in a post titled Days of the Year and Gematria back in August of 2021. The idea behind this sequence reminds me of my own approach described in a blog post titled Consolidating Fibonacci-like Numbers where I considered numbers whose digits following a Fibonacci pattern e.g. 21347:$$21347 \text{ where }2 + 1 =3, 1+3=4,3+4=7$$However, getting back to approach followed in OEIS A129938, an interesting "spin-off" could be that previously unnamed tribonacci sequences could be given memorable names. For example, using Table 1 we could write:$$ \text{ cat } \rightarrow \text{ c, a, t } \rightarrow \text{ 3, 1, 20 }$$and so the "cat" sequence becomes:$$3, 1, 20, 24, 45, 79, \dots$$Similarly we have:$$ \text{ dog } \rightarrow \text{ d, o, g } \rightarrow \text{ 4, 15, 7 }$$ So the "dog" sequence becomes:$$4, 15, 7, 26, 48, 81, \dots$$Silly I know but it would make for an interesting puzzle in Puzzle of the Day. The sequence doesn't have to be tribonacci, it could simply be Fibonacci-like. For example, we could ask why is the sequence 13, 5, 18, 23, 41, 65, ... egocentric? The answer is that:$$13, 5 \rightarrow \text{ m, e } \rightarrow \text{ me }$$Similarly, the sequence could be made of four or more seeds and a puzzle created. For example, we could ask what does this sequence 13, 9, 12, 11, 45, 77, ... and the Milky Way have in common? The answer is that the first four members of the sequence are the seeds to generate the future members of the sequence and we have:$$ 13, 9, 12, 11 \rightarrow \text{ m, i, l, k } \rightarrow \text{ milk}$$That's enough nonsense for the moment but let's not forget that there has always been a long-standing connection between letters of certain alphabets (Hebrew, Ancient Greek and Arabic for example) and numbers. With the English language the connection has weakened but it's still there and not just in the way shown in Table 1. There are other ways to assign values to letters in the English alphabet. Table 2 shows an alternative way that is more in keeping with the ancient languages.
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Table 2: source |
