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SteinhausMoser Notation is a well know notation created by Hugo Steinhaus, and extended by Leo Moser.
My intention in this post is to show the resolution of some 2's inside polygons of SteinhausMoser notation. ItÂ´s well know that the first polygon is the triangle, and any number \(n\) inside a triangle is converted to the \(n\) power of \(n\) or \(n^{n}\).
Here we represent a value \(n\) inside a triangle as \(n[3]_{1}\), according the general notation proposed by Susan Stepney. The notation extends to:
 â€‹\(n\) inside a square or \(n[4]_{1}\) = \(n\) inside \(n\) triangles = \(n[3]_{n}\);
 \(n\) inside a pentagon or \(n[5]_{1}\) = \(n\) inside \(n\) squares = \(n[4]_{n}\);
 \(n\) inside a hexagon or \(n[6]_{1}\) = \(n\) inside \(n\) pentagons = \â€¦

Sumselfgogopyr is defined as the summation of the nth ngonal pyramidal numbers with n from 3 to gogopyr, the term was coined by Daniel CorrÃªa.
Sumselfgogopyr is computed as described below:
\(Sumselfgogopyr = \sum^{gogopyr}_{n=3} \frac{3 \cdot n^{2} + n^{3} \cdot (n2)  n \cdot (n5)}{6}\)
Sumselfgogopyr has 1995 digits, and according to the calculations using BCalc to convert gogopyr to power of 10 notation, and using WolframAlphato perform the calculation with the maximum input length, the approximated form of sumselfgogopyr is:
\(Sumselfgogopyr \approx 4.28669410150... \times 10^{1994}\)
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Selfgogopyr is defined as the gogopyrth gogopyrgonal pyramidal number. The term was coined by Daniel CorrÃªa.
Selfgogopyr is computed using the general formula for an rgonal pyramidal number described below:
\([3.n^{2} + n^{3}.(r2)  n.(r5)]/6\)
where \(r = n = gogopyr\).
Selfgogopyr has 1597 digits, and according to the calculations performed using BCalc configured to show 2011 digits, the full decimal form is:
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Sumgogopyr is defined as the summation of the nth ngonal pyramidal numbers with n from 3 to googol, the term was coined by Daniel CorrÃªa.
Sumgogopyr is computed as described below:
\(Sumgogopyr = \sum^{googol}_{n=3} \frac{3 \cdot n^{2} + n^{3} \cdot (n2)  n \cdot (n5)}{6}\)
In its decimal form, sumgogopyr has 499 digits as described: 3 as the first 299 digits followed by the digit 8 followed by a sequence of 99 3's followed by the digit 7 followed by a sequence of 98 9's, and 6 as the last digit.
The full decimal form of sumgogopyr is expressed below:
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Gogopyr is defined as the googolth googolgonal pyramidal number. The term was coined by Daniel CorrÃªa.
Gogopyr is computed using the general formula for an rgonal pyramidal number described below:
\([3.n^{2} + n^{3}.(r2)  n.(r5)]/6\)
where \(r = n = 10^{100}\).
In its full decimal form, gogopyr has 400 digits as described: 1 as the first digit followed by 99 6's in sequence followed by 100 3's in sequence followed by 99 6's in sequence followed by the digits 7 and 5, and finally followed by 99 0's in sequence.
The full decimal form of gogopyr is expressed below:
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