Definition:Reversal
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Definition
Let $m = \sqbrk {a_n a_{n - 1} a_{n - 2} \ldots a_2 a_1 a_0}$ be an integer expressed in base $10$.
That is:
- $m = \ds \sum_{k \mathop = 0}^n a_k 10^k$
Its reversal $m'$ is the integer created by writing the digits of $m$ in the opposite order:
- $m' = \sqbrk {a_0 a_1 a_2 \ldots a_{n - 2} a_{n - 1} a_n}$
That is:
- $m' = \ds \sum_{k \mathop = 0}^n a_{n - k} 10^k$
Also known as
Some sources use reverse.
Some sources use the term mirror.
Also see
- Results about reversals can be found here.
Sources
- Nov. 2015: Jessie Byrnes, Chris Spicer and Alyssa Turnquist: The Sheldon Conjecture (Math Horizons Vol. 23: pp. 12 – 15) www.jstor.org/stable/10.4169/mathhorizons.23.2.12
- Feb. 2019: Carl Pomerance and Chris Spicer: Proof of the Sheldon Conjecture (Amer. Math. Monthly Vol. 121, no. 1: pp. 1 – 10)
- Weisstein, Eric W. "Reversal." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Reversal.html