A212794 Triangular numbers (A000217) which are also hypotenuse numbers (A009003).

10, 15, 45, 55, 78, 91, 105, 120, 136, 153, 190, 210, 300, 325, 351, 406, 435, 465, 561, 595, 630, 666, 703, 741, 780, 820, 861, 990, 1035, 1225, 1275, 1326, 1378, 1431, 1485, 1540, 1653, 1711, 1770, 1830, 1891, 2080, 2145, 2278, 2346, 2415, 2485, 2628

Offset: 1

Author

M. F. Hasler, May 27 2012

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A000217 and A009003.

Programs

Maple

ishyp:= proc(n) ormap(t -> t mod 4 = 1, numtheory:-factorset(n)) end proc:
select(ishyp, [seq(i*(i+1)/2, i=1..100)]); # Robert Israel, Jun 02 2023

Mathematica

A212794list[upto_]:=Select[PolygonalNumber[Range[4,upto]],AnyTrue[Map[Mod[First[#],4]==1&,FactorInteger[#]],TrueQ]&];A212794list[100] (* Paolo Xausa, Jul 28 2023 *)

PARI

for(n=1,99, is_A009003(A000217(n)) & print1(A000217(n)","))

PARI

is_A212794(n) = is_A000217(n) & is_A009003(n)