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Search: id:A106660
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| A106660 |
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A triangle with sides that are three consecutive integers has an area that is a prime after rounding. The first of the consecutive numbers gives the sequence. |
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+0
1
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| 2, 11, 14, 17, 29, 31, 40, 47, 48, 94, 96, 98, 106, 111, 116, 118, 126, 144, 171, 172, 173, 178, 179, 188, 206, 216, 237, 238, 245, 246, 261, 265, 282, 284, 298, 317, 320, 326, 355, 366, 371, 376, 428, 442, 470, 496, 556, 560, 562, 570, 587, 605, 609, 613, 620
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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Simply pass three consecutive integers through the formula that gives the area of a triangle from the three sides.
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EXAMPLE
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For triangle of sides 17,18,19 the formula gives 139.4 and this rounds to a prime.
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MAPLE
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Digits := 60 : isA106660 := proc(p) local q, r, s, area ; q := p+1 ; r := q+1 ; s := (p+q+r)/2 ; area := round(sqrt(s*(s-p)*(s-q)*(s-r))) ; RETURN(isprime(area)) ; end: for n from 1 to 900 do if isA106660(n) then printf("%d, ", n) ; fi ; od : - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2007
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CROSSREFS
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Sequence in context: A041163 A073914 A041971 this_sequence A130288 A031192 A034039
Adjacent sequences: A106657 A106658 A106659 this_sequence A106661 A106662 A106663
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KEYWORD
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nonn
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AUTHOR
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J. M. Bergot (thekingfishb(AT)yahoo.ca), May 19 2007
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2007
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