What is your one-liner for getting 2023? Comment below!
DOWNLOAD-DESKTOP-NOTEBOOK.nb (31.6 KB)
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A few more
LinearRecurrence[{3, -3, 1}, {7, 34, 79}, 15] // Last
LinearRecurrence[{0, 1, 1, 2}, {0, 2, 3, 10}, 17] // Last
LinearRecurrence[{4, 0, -5, -2}, {0, 2, 10, 41}, 7] // Last
N[FromContinuedFraction[Flatten[{44, Table[{1, 43, 1, 88}, 5]}]]^2, 40]
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Also can be checked in Wolfram|Alpha: 7^7 mod 7! - Wolfram|Alpha
BTW - Cool idea! Here is something very simple:
2^{11}-5^2 = 2023
In[]:= 2^11-5^2
Out[]= 2023
And thanks to John Conway’s discovery of 1988 that e^{\pi }-\pi \approx 20 we have
\text{Round}\left[101 e^{\pi }-100 \pi \right]= 2023
In[]:= Round[101*E^Pi-100*Pi]
Out[]= 2023
I am trying to find some exact ones based on Golden Ratio, Pi, E, other irrational and transcendental numbers. Similar to Fibonacci sequence formula, but much neater than this (I hope someone will figure this out):
\frac{\phi ^{18}-(1-\phi) ^{18}}{\sqrt{5}}-3 \cdot 11 \cdot 17=2023
In[]:= FullSimplify[(GoldenRatio^18-(1-GoldenRatio)^18)/Sqrt[5]-3 11 17]
Out[]= 2023
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Going into algebraic number theory
-NumberFieldDiscriminant[x /. Solve[x^3 == x^2 + 6 x + 5][[1]]]
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With this:
I thought it would be interesting to see what could be one in base 7 to get to 2023.
https://www.wolframalpha.com/input?i=decimal+form+of+7*23_7%5E2
Or in WL:
7 7^^23^2
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There are some good answers in comments on Reddit Math: Reddit
Also there is this link with the properties: Properties of number 2023
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I prefer to look forward to what 2023 might bring to us!
2023 is a very interesting 3-color totalistic cellular automaton:
ArrayPlot[CellularAutomaton[{2023,{3,1}},{{1},0},500],ColorRules->{0->White,1->Gray,2->Red}]
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3^2+7^2+11^2+15^2+19^2+23^2+27^2 = 2023
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Not a formal per se but 2023 is a multiple of 7 whose digits also add to 7. In other words 2023 is the numbers congruent to 7 mod 63.
Looks like we got another interesting postcard post by Fermat’s Library on LinkedIn:
which is in Wolfram:
In[]:= (10+(9+8*7)*6)*5+4*3*2-1
Out[]= 2023
I wonder is it easy to find such combination? How many numbers we can get out of specific range using a specific set of operations? And how many combinations we have for a single number on average?
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From a Tweet by Srinivasa Raghava (he also shared a number of other interesting results of 2023):
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If we allow concatenation.
1*2*3*456+7-8*9*10
1+2*34*5*6-7+8-9-10
1/2*345*6+78+910
12+3/4*5*67*8-9+10
12/34*5678+9+10
12+345*6-78+9+10
10-9*8-76+5*432+1
10-9*87+65*43+2-1
10*98-7*6+543*2-1
10*987/6+54/3*21
1 Like
[ (2023)^2 - 2023 ] / [6* (2023)] = 337
New year : 337 *(6) + 1 = 2023
or [337 (7) (2023)] / 2023] - 338 = 2023
Last year : 337 (6) = 2022
or 337(7) - 337 = 2022
Moving along : 337 + 1 = 338
Finding the next primes using the formula above :
[ [2023 * ( 338)* (7) - 2023] / 2023] - 338 = 2027 is prime
[ [2023 ( 338) (7) + 2023] / 2023] - 338 = 2029 is prime
[(2029+338) 2023 - 2023 / (2366)] = 2023
[(2027+338) 2023 -+2023 / (2366)] = 2023
2023 within a solution using the next twin primes
= (11/x+1 )^-1
which = 184
184 * 11 - 1 = 2023