|
| |
|
|
A106660
|
|
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.
|
|
0
| |
|
|
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; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
FORMULA
| Simply pass three consecutive integers through the formula that gives the area of a triangle from the three sides.
|
|
|
EXAMPLE
| For triangle of sides 17,18,19 the formula gives 139.4 and this rounds to a prime.
|
|
|
MAPLE
| 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
|
|
|
MATHEMATICA
| With[{c=Sqrt[3]/4}, Select[Range[700], PrimeQ[Floor[1/2+c Sqrt[#^2 (#^2-4)]]]&] -1] (* From Harvey P. Dale, Oct 25 2011 *)
|
|
|
CROSSREFS
| Sequence in context: A041163 A073914 A041971 * A130288 A031192 A034039
Adjacent sequences: A106657 A106658 A106659 * A106661 A106662 A106663
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| J. M. Bergot (thekingfishb(AT)yahoo.ca), May 19 2007
|
|
|
EXTENSIONS
| Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2007
|
| |
|
|
