A212794 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

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 *)

(* Alternative: *)

With[{hn=Select[Range[3000], SquaresR[2, #^2]>4&]}, {c=Floor[(Sqrt[8 Max[hn]+1]-1)/2]}, {tn=Accumulate[Range[c]]}, Intersection[hn, tn]] (* Harvey P. Dale, Aug 25 2026 *)

PROG

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

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

CROSSREFS

Intersection of A000217 and A009003.

Sequence in context: A372044 A261853 A259629 * A048061 A188651 A330203

Adjacent sequences: A212791 A212792 A212793 * A212795 A212796 A212797

KEYWORD

nonn,changed

AUTHOR

M. F. Hasler, May 27 2012

STATUS

approved