One day, one decomposition
A001463: Partial sums of A001462; also a(n) is the last occurrence of n in A001462

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A001463.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A001463.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A001463.html

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One day, one decomposition
A000378: Sums of three squares: numbers of the form x^2 + y^2 + z^2

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A000378.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A000378.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A000378.html

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How did Rachel Reeves make her sums add up?

The Chancellor has announced welfare and spending cuts to try to restore her £9.9bn "headroom", so she can meet her rules on the economy. BBC Verify's Ben Chu looks at how she's made her sums add up. Produced by Jemimah Herd. Motion graphics by Mesut Ersoz. #Rachel #Reeves #sums #add

https://10bmnews.com/2025/03/how-did-rachel-reeves-make-her-sums-add-up/

So, I learned something this past weekend about sequential exponential numbers, and how they can be verified through addition and subtraction no matter how high the exponents go.

Is this a known thing?

For example:

Every sequential ^2 has a once nested difference that increases by 2 and it's every odd number.

Every sequential ^3 has a twice nested difference of 6, which the first set of differences create a number which must then be subtracted from the next difference to see this pattern.

Every sequential ^4 has a thrice nested difference of 24, which the first set of differences create a number which must then be subtracted from the next set, followed by the third set to see this pattern.

Every sequential ^5 has a quaternary nested difference of 120, which means requires subtracting the sets four times to see the pattern.

So this validates ^6 at the fifth set of differences will provide a pattern of 720, ^7 at the sixth set will provide a pattern of 5040 and so on.

What is this called? Is there a simplified equation that shows this? Any and all help is much appreciated. Thanks!

#math #sums #difference #factors #equations #patterns #validation #mathematics #solve #question #puzzle #howdoifindthename

One day, one decomposition
A122616: Sums of 5th powers of primes

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A122616.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A122616.html

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One day, one decomposition
A072502: Numbers that are run sums (trapezoidal, the difference between two triangular numbers) in exactly 3 ways

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A072502.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A072502.html

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