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.

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

Offset

1,1

Links

Table of n, a(n) for n=1..55.

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, Jun 08 2007

Mathematica

With[{c=Sqrt[3]/4}, Select[Range[700], PrimeQ[Floor[1/2+c Sqrt[#^2 (#^2-4)]]]&] -1] (* Harvey P. Dale, Oct 25 2011 *)

Crossrefs

Sequence in context: A266991 A041971 A299531 * A130288 A287395 A031192

Adjacent sequences: A106657 A106658 A106659 * A106661 A106662 A106663

Keyword

nonn

Author

J. M. Bergot, May 19 2007

Extensions

Corrected and extended by R. J. Mathar, Jun 08 2007

Status

approved