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Search: id:A072330
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| A072330 |
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Common difference n such that primitive triangles exist which are n-arithmetic (i.e. primitive Heronian triangles whose sides in A.P. have common difference n). |
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+0
8
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| 1, 11, 13, 23, 37, 47, 59, 61, 71, 73, 83, 97, 107, 109, 121, 131, 143, 157, 167, 169, 179, 181, 191, 193, 227, 229, 239, 241, 251, 253, 263, 277, 299, 311, 313, 337, 347, 349, 359, 373, 383, 397, 407, 409, 419, 421, 431, 433, 443, 457, 467, 479, 481, 491, 503
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The first entry in particular is associated with sequences A003500 and A007655.
Such a triangle has a middle side 2*x partitioned into x +/- 2*n by the corresponding altitude (i.e. median and altitude points are always a distance 2*n apart).
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REFERENCES
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R. A. Beauregard & E. R. Suryanarayan, Arithmetic Triangles, Mathematics Magazine pp. 105-115 70(2) 1997 MAA.
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FORMULA
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n = 1 or a product of primes p congruent to +/- 1 (mod 12).
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CROSSREFS
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Cf. A072360, A086909, A089019, A089020, A096672, A096673, A096674.
Adjacent sequences: A072327 A072328 A072329 this_sequence A072331 A072332 A072333
Sequence in context: A048393 A136058 A106073 this_sequence A097933 A127043 A084952
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KEYWORD
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nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 15 2002
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EXTENSIONS
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Corrected and extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jul 02 2004
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