

A336753


Largest side of integersided 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
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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 integersided triangles such that b = (a+c)/2 with a < c.
c >= 4 and each largest side c appears floor((c1)/3) = A002264(c1) 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 B290 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 bfloor((b1)/2) to b1 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



