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Grafting Number


A grafting number, in the original decimal square root convention, is a nonnegative integer whose digits appear as a consecutive block in the decimal expansion of its square root, starting either in the integer part or immediately after the decimal point (Numberphile 2012; Tanniru 2015, pp. 309-310). The decimal point is ignored when matching the block. For example,

 sqrt(98)=9.8994949366...,

whose first two digits reproduce 98 across the decimal point. Similarly, sqrt(77)=8.7749643873... begins its fractional part with 77, while sqrt(764)=27.6405499221... contains 764 beginning at the units place.

Tanniru (2015, p. 309) calls these integers grafting integers and uses grafting numbers for a broader construction involving real numbers, other nth roots, and other number bases. This distinction matters when comparing the original integer examples with the generalized terminology.


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References

Numberphile. "98 and Grafting Numbers." Jan. 20, 2012. https://www.youtube.com/watch?v=hiOMtBrH8pc.Tanniru, R. "A Short Note Introducing Grafting Numbers and Their Connection to Catalan Numbers." J. Combin. Math. Combin. Comput. 95, 309-321, 2015. https://combinatorialpress.com/article/jcmcc/Volume%20095/vol-095-paper%2021.pdf.

Cite this as:

Weisstein, Eric W. "Grafting Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GraftingNumber.html

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