login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A336753 Largest side of integer-sided triangles whose sides a < b < c are in arithmetic progression. 5
4, 5, 7, 6, 8, 7, 10, 9, 8, 11, 10, 9, 13, 12, 11, 10, 14, 13, 12, 11, 16, 15, 14, 13, 12, 17, 16, 15, 14, 13, 19, 18, 17, 16, 15, 14, 20, 19, 18, 17, 16, 15, 22, 21, 20, 19, 18, 17, 16, 23, 22, 21, 20, 19, 18, 17, 25, 24, 23, 22, 21, 20, 19, 18, 26, 25, 24, 23, 22, 21, 20, 19 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The triples of sides (a,b,c) with a < b < c are in increasing order of perimeter = 3*b, and if perimeters coincide, then by increasing order of the smallest side. This sequence lists the c's.

Equivalently: largest side of integer-sided triangles such that b = (a+c)/2 with a < c.

c >= 4 and each largest side c appears floor((c-1)/3) = A002264(c-1) times but not consecutively.

For each c = 5*k, k>=1, there exists exactly one right triangle (3*k, 4*k, 5*k) whose sides a < b < c are in arithmetic progression.

For the corresponding primitive triples and miscellaneous properties and references, see A336750.

REFERENCES

V. Lespinard & R. Pernet, Trigonométrie, Classe de Mathématiques élémentaires, programme 1962, problème B-290 p. 121, André Desvigne.

LINKS

Table of n, a(n) for n=1..72.

FORMULA

a(n) = A336750(n, 3).

EXAMPLE

c = 4 only for the smallest triangle (2, 3, 4).

c = 5 only for Pythagorean triple (3, 4, 5).

c = 6 only for triple (4, 5, 6).

c = 7 for the two triples (3, 5, 7) and (5, 6, 7).

MAPLE

for b from 3 to 30 do

for a from b-floor((b-1)/2) to b-1 do

c := 2*b - a;

print(c);

end do;

end do;

CROSSREFS

Cf. A336750 (triples), A336751 (smallest side), A307136 (middle side), this sequence (largest side), A336754 (perimeter).

Cf. A335896 (largest side when triangles angles are in arithmetic progression).

Sequence in context: A016720 A104140 A003563 * A023833 A151551 A021690

Adjacent sequences:  A336750 A336751 A336752 * A336754 A336755 A336756

KEYWORD

nonn

AUTHOR

Bernard Schott, Aug 25 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 6 00:46 EDT 2021. Contains 346493 sequences. (Running on oeis4.)