When interpreted as hexadecimal, the number 147 corresponds to the Unicode character:

# Ň

(U+0147 LATIN CAPITAL LETTER N WITH CARON)

~~Alternatively, the number of tries it felt like it took to post this.~~

When interpreted as hexadecimal, the number 147 corresponds to the Unicode character:

(U+0147 LATIN CAPITAL LETTER N WITH CARON)

~~Alternatively, the number of tries it felt like it took to post this.~~

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[NAE}I was hoping to get 144, and did!

Regarding 145, I know more music theory than the average robotics nerd, having taken a high school music theory class, being in my in my 37th year as a US Navy acoustician, and being an avid amateur mathematician who really likes good rational approximations of irrational numbers, including twelfth roots of two. But it was not enough for me to make sense of the 145 post cold, because I had never encountered the Roman numeral notation. After about three minutes of web searches (plus my background] it clicked, so I’ll break it down before I work on my next entry.

I’ll start assuming you don’t know any music theory and are willing to trust me in a few places about music, but have basic high school math skills. @Shiven or anyone else, please feel free to correct me; I’d rather be embarrassed and learn something than leaving all of CD (including myself) with a misconception.

It’s a serious wall of text, so I’ll hide it, but before going inside “hidden” where LaTeX doesn’t work, I’ll define \eta=\sqrt[12]{2}\approx1.05946.

I’ll pop forward to modern understanding of sound and music, but tie it back to ancient understanding fairly quickly.

**Frequency and Ratios**

Frequency is the number of times per second (or other time unit) that a pure note of sound (sin(t) or cos(t) or a linear combination of them) returns to the same state, with the same pressure and same direction of pressure change.

In the case of strings (and also approximately many other instruments), with other things equal (in this case the size and material of the string and its tension) the lowest frequency produced by excitation (plucking or strumming) is inversely proportional to the length, so even though the ancients couldn’t measure frequency, they could use length of a string and understood this, just in reciprocal form.

Going back thousands of years, it was found that notes with frequencies or string lengths in small integer ratios pleased the ear, while those with large ratios or truly irrational were unpleasant. This is apparently because even if we can’t hear the gcd(f1,f2), our brain infers that this “fundamental” frequency is probably there, just inaudible, and these are harmonics, or multiples of the fundamental. For an example of unpleasant, play F & B at the same time, the two white keys on a piano with three black keys between them. For pleasant, Try E and B, moving the left of those two one key further left.

Then, a convenient mathematical strangeness pops up. It turns out that every proper ratio with a denominator no more than six can be approximated pretty well by a negative integer power of η, the twelfth root of two. As a few examples, η⁻⁷≈0.66742≈2/3, η⁻⁵≈0.74915≈3/4, η⁻⁴≈0.79370≈4/5, η⁻³≈.084090≈5/6, and of course η⁻¹²=1/2. It is only this crazy coincidence which allows instruments tuned to different keys to play well together. It’s a good enough approximation to trigger the harmonic detectors in most if not all human brains.

**Chords and Keys**

A major chord is three notes played simultaneously with ratios of 4:5:6. This is approximated well with η^ [0 4 7]. A major key has eight notes per octave (factor of 2) which repeat, so I’ll extend to nine for clarity in ratios of approximately η^ [0 2 4 5 7 9 11 12 14].

A minor chord is three notes played simultaneously with ratios of 10:12:15, approximated well with η^ [0 3 7]. A minor key has eight notes per octave which I’ll again extend to nine in ratios of approximately η^ [0 2 3 5 7 8 10 12 14].

By inspection, the major chords of the first, fourth, and fifth notes of the major key all fit the major key, and also the minor chords of the first, fourth, and fifth notes fit in the minor key. By “fit”, as an example, add 7, the fourth exponent of the major key to the major chord, and you get 7, 11, and 14, all of which are in the major key.

The whole thing with Roman numerals is that Roman numerals have upper and lower case, so 1 4 and 5 are designated I, IV, and V because their chords fit in the key, while 2, 3, 6, 7, and 8 are ii, iii, vi, vii, and viii as they do not.

Hey, I learned something new today, and explained it (because you don’t REALLY understand something until you explain it to someone else)! That’s going in weekly wins.

[/NAE]

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Dunbar’s Number, an estimate of the maximum number of friendships a human can comfortably maintain, based on brain size and extrapolated from other apes. (148)

The result of the following python script:

```
ord(min(str(not(not()))))+ord(str(next).upper()[int(len(str(iter))/int(len(vars(__builtins__))/ord(min(str(not(not()))))))])+int(min(str(ord(min(str(not(not()))))+ord(str(next).upper()[int(len(str(iter))/int(len(vars(__builtins__))/ord(min(str(not(not()))))))])+int(min(str(ord(min(str(not(not()))))))))))
```

(149)

Edit: Tested on Python 3.9 and 3.12.6. Works despite python gaining 6 new builtins during that time.

\prod_{k=1}^3 p_k^{\lfloor \frac{P_k}2 \rfloor}, where p_k is the k’th prime number.

\prod_{k=1}^3 p_k^{\lfloor \frac{P_k}2 \rfloor}=2^{\lfloor \frac22 \rfloor}3^{\lfloor \frac32 \rfloor}5^{\lfloor \frac52 \rfloor}=2^13^15^2=2\centerdot3\centerdot25=150

The amount of playoff wins Patrick Roy had in his career (151)

Chikorita, 1st pokemon in Gen 2 pokedex (152)

The number of fish caught in the Gospel of John 21:11. (153)

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The JavaScript version:

```
console.log(String.fromCharCode([...Array(Array.from(String(!!(Math.sin(Math.PI / 2) === 1))).map((c, i) => i > 0 ? c.charCodeAt(0) : c.toUpperCase().charCodeAt(0)).reduce((a, b) => Math.min(a, b))).keys()].reduce((a, b) => a + b, 0)));
```

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CLIV

154 in Roman Numerals

\sum_{k=1}^35^k=5+25+125=155

\sum_{k=0}^35^k [Just Kidding]

The number of hourly chimes or cuckoos from a clock in twenty four hours. 2(1+2+3+4+5+6+7+8+9+10+11+12)=156

The only base 12 repunit prime with only three digits, also the second base 12 repunit prime (157)

The model number of the first monocoque Formula 1 car produced by Ferrari (in 1964).

Working base 15, the only two digit number which is equal to the sum of the squares of the digits in its square. (159)

159_{10}=A9_{15}

A9_{15}^2=7756_{15}

7^2+7^2+5^2+6^2=A9_{15}=159_{10}

The only one digit numbers filling this are zero and one, and the only three digit numbers are: 129_{15}=264_{10}; 13E_{15}=284_{10} ; 156_{15}=306_{10}; 1AC_{15}=387_{10}. It is easy to prove there are no 4 digit or larger numbers, even though oeis hasn’t gotten word [I’m working to fix that].

The sum of the cube of the first 3 prime numbers:

2^3 + 3^3 + 5^3 = 160

I need to figure out how the rest of you guys are able to actually write equations in here.

161: Hexagonal pyramidal number.

@wgorgen : you can use LaTeX to write equations, just enclose it with $.

The number of games in a Major League Baseball regular season since the early 1960’s, excluding strike and pandemic years. (162)

@wgorgen, select one of the posts with LaTeX in it, and quote it to see what the markup looks like.

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The 38th prime number (163)

The number of beige squares on a S_1C_3R_1A_1B_3B_3L_1E_1 board.

There are 8 red triple word scores, 17 pink double word scores, 12 bold blue triple letter scores, and 24 pastel blue double letter scores, and 15^2=225 total squares. 225-8-17-12-36=164.

There are an infinity of hexagonal pyramidal numbers. To uniquely identify 161, you should say the 6th hexagonal pyramidal number.

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