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Squarian digits
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Squarian digits (pronounced either "sqwarey-an" or "scwarry-an") were recently discovered and named by Dr. Anthony Harrington, Squarian digits are a 9 numbered sequence made up of digit routes that can be used to work out the proceeding square number. The sequence is 149779419. (Note: due to the sudden discovery, there is little, if any, reference material available online. Any documents of reference are in fact unnecessary as all proof of the sequence and theory can be judged below.) Examples of usage Examples 29 x 29 = 841 -- 8 + 4 + 1 = 13, digit route is 4. 30 x 30 = 900 -- digit route is 9. Therefore, by looking at the sequence: 31 x 31 is a number in the 900's, it's digit route is 7, and because the (1 x 1) in the units column makes 1, the last digit is one. Therefore the number is 9_1 but it must add to make 7. I.e. 9 + 1 + 6 = 16, 1 + 6 = 7. Thus, 31 x 31 = 961. Use of the Sequence Although square numbers are a seldom discussed topic, as viewable when one uses a search engine such as Google to find this sequence; it was discovered in the hopes of aiding future mathematical endeavors, particularly where shortcuts and "tricks" would be appreciated. Arguably however, calculators are far more efficient not to mention faster, but in such examinations where a calculator is not permitted, it's purpose shall be fulfilled most adamantly. Squares of 3 digit numbers As of yet, the sequence has not been tested into the squaring of 3 digit numbers. It is therefore pertinent to carry out such a test below, using the data gathered, with 99 as a control: 99 x 99 = 9801, 9+8+0+1 = 18, digit route is 9. 100 x 100 = 10000, digit route is 1. Using the sequence and following it from left to right continuously, 149779419, the next digit route should be 4. 101 x 101 = 10201, digit route 4. Limitations The sequence has not had it's limitations established, but many perceive that it works perfectly fine for all integers proceeding from -∞ to +∞ The sequence itself is up for deliberation on whether it should be added to mathematic reference literature at a date currently unknown. See Also
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