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Search: id:A106171
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| A106171 |
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A triangle with three consecutive primes as sides has an area that is a prime after rounding. The sequence gives the first of the three consecutive primes. |
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+0
3
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| 5, 11, 23, 59, 71, 89, 211, 239, 269, 349, 389, 419, 431, 467, 479, 521, 571, 577, 647, 863, 983, 1087, 1213, 1223, 1733, 1747, 1759, 1933, 1949, 1973, 2131, 2297, 2411, 2521, 2659, 2879, 2909, 2999, 3011, 3191, 3203, 3209, 3391, 3467, 3469, 3517, 3559
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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Simply use the formula for the area of a triangle given the three sides.
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EXAMPLE
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For sides 5,7,11 the formula gives 12.96 and with rounding this becomes 13, a prime.
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MAPLE
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s:=proc(n) local a, b, c, p, A: a:=ithprime(n): b:=ithprime(n+1): c:=ithprime(n+2): p:=(a+b+c)/2: A:=sqrt(p*(p-a)*(p-b)*(p-c)): if isprime(round(A))=true then a else fi end: seq(s(n), n=1..700); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 25 2007
Digits := 60 : isA106171 := proc(p) local q, r, s, area ; if isprime(p) then q := nextprime(p) ; r := nextprime(q) ; s := (p+q+r)/2 ; area := round(sqrt(s*(s-p)*(s-q)*(s-r))) ; RETURN(isprime(area)) ; else false ; fi ; end: for n from 1 to 900 do p := ithprime(n) : if isA106171(p) then printf("%d, ", p) ; fi ; od : - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2007
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CROSSREFS
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Adjacent sequences: A106168 A106169 A106170 this_sequence A106172 A106173 A106174
Sequence in context: A046138 A024829 A097279 this_sequence A059455 A095030 A065114
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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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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu) and R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 25 2007
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