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%I #16 Jul 29 2023 05:04:37
%S 10,15,45,55,78,91,105,120,136,153,190,210,300,325,351,406,435,465,
%T 561,595,630,666,703,741,780,820,861,990,1035,1225,1275,1326,1378,
%U 1431,1485,1540,1653,1711,1770,1830,1891,2080,2145,2278,2346,2415,2485,2628
%N Triangular numbers (A000217) which are also hypotenuse numbers (A009003).
%H Robert Israel, <a href="/A212794/b212794.txt">Table of n, a(n) for n = 1..10000</a>
%p ishyp:= proc(n) ormap(t -> t mod 4 = 1, numtheory:-factorset(n)) end proc:
%p select(ishyp, [seq(i*(i+1)/2, i=1..100)]); # _Robert Israel_, Jun 02 2023
%t A212794list[upto_]:=Select[PolygonalNumber[Range[4,upto]],AnyTrue[Map[Mod[First[#],4]==1&,FactorInteger[#]],TrueQ]&];A212794list[100] (* _Paolo Xausa_, Jul 28 2023 *)
%o (PARI) for(n=1,99, is_A009003(A000217(n)) & print1(A000217(n)","))
%o (PARI) is_A212794(n) = is_A000217(n) & is_A009003(n)
%Y Intersection of A000217 and A009003.
%K nonn
%O 1,1
%A _M. F. Hasler_, May 27 2012
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