A125302 Nonprime numbers n such that n cannot be a semiperimeter of an integer Heronian triangle.

1, 4, 10, 14, 26, 46, 51, 58, 62, 69, 74, 92, 94, 106, 122, 123, 141, 142, 158, 188, 202, 206, 213, 218, 254, 267, 284, 298, 302, 314, 329, 334, 339, 346, 355, 362, 365, 382, 394, 398, 411, 446, 458, 478, 485, 501, 526, 538, 542, 554, 573, 586, 622, 634, 668

Offset

1,2

Comments

Trivially, no prime number can be a semiperimeter of an integer Heronian triangle. Therefore primes are excluded from the sequence.

Links

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

Eric Weisstein's World of Mathematics, Heronian Triangle.

Maple

notriangle:=proc(n::nonnegint) local a, b, c; if type(n, prime) then RETURN(false) fi; for a from floor(2*n/3) to n-1 do for b from floor(n-a/2) to a do c:=2*n-a-b; if type(sqrt(n*(n-a)*(n-b)*(n-c)), integer) then RETURN(false); fi; od; od; RETURN(true); end: N:=100: a:=array[1..N]: i:=0: n:=0: while i<N do n:=n+1; if notriangle(n) then i:=i+1; a[i]:=n; fi; od: seq(a[i], i=1..N);

Crossrefs

Sequence in context: A051741 A022382 A162521 * A365679 A175588 A239788

Adjacent sequences: A125299 A125300 A125301 * A125303 A125304 A125305

Keyword

nonn

Author

Seppo Mustonen, Jan 17 2007

Status

approved