A197040 Occurrences of edge-lengths of Euler bricks in every 100 consecutive integers.
3, 8, 9, 8, 9, 9, 6, 9, 10, 8, 7, 9, 6, 8, 7, 8, 11, 6, 7, 8, 9, 8, 7, 6, 8, 10, 6, 6, 6, 8, 8, 8, 8, 9, 6, 9, 7, 6, 7, 8, 8, 9, 7, 11, 7, 8, 5, 9, 8, 9, 9, 7, 6, 7, 9, 6, 7, 9, 7, 8, 10, 5, 9, 7, 7, 7, 7, 6, 9, 9, 6, 8, 7, 9, 8, 6, 9, 5, 9, 9, 8, 6, 6, 7, 7
Offset: 1
Examples
For n=1 (i.e., the integers 1..100), there are only 3 possible edge-lengths for Euler bricks: 44, 85, 88.
References
- L. E. Dickson, History of the Theory of Numbers, vol. 2, Diophantine Analysis, Dover, New York, 2005.
- P. Halcke, Deliciae Mathematicae; oder, Mathematisches sinnen-confect., N. Sauer, Hamburg, Germany, 1719, page 265.
Links
- Robin Visser, Table of n, a(n) for n = 1..10000
- E. W. Weisstein, MathWorld: Euler brick
Crossrefs
Programs
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Sage
def a(n): ans = set() for x in range(100*(n-1)+1, 100*n+1): divs = Integer(x^2).divisors() for d in divs: if (d <= x^2/d): continue if (d-x^2/d)%2==0: y = (d-x^2/d)/2 for e in divs: if (e <= x^2/e): continue if (e-x^2/e)%2==0: z = (e-x^2/e)/2 if (y^2+z^2).is_square(): ans.add(x) return len(ans) # Robin Visser, Jan 02 2024
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