%I #27 Jun 25 2022 13:19:32
%S 3,253,595,703,2211,2485,4753,13695,22791,23005,35245,52003,54285,
%T 62835,82215,88831,119805,173755,219453,238395,252405,271953,275653,
%U 306153,325221,350703,406351,470935,482653,521731,607753,611065,634501,661825,675703,726615
%N Triangular numbers whose binary conversion, read in decimal, is prime.
%H K. D. Bajpai and Charles R Greathouse IV, <a href="/A227028/b227028.txt">Table of n, a(n) for n = 1..10000</a> (first 116 terms from Bajpai)
%e A000217(22) = 253 = 11111101_2, and 11111101_10 is prime, so 253 is a term.
%p with(numtheory):with(StringTools):
%p #=Triangular numbers whose binary conversion is prime when read in decimal.
%p PRS:= proc(x,y)
%p local i,a,b,c,count;
%p count:=1;
%p for i from x to y do;
%p a:=(1/2)*(i)*((i)+1);
%p b:=convert(a,binary);
%p c:=isprime(b);
%p if c then lprint(count,a); count:=count+1; fi; od;
%p lprint("Finished "):
%p end:
%p PRS(1,5000);
%o (PARI) isA036952(n)=my(v=binary(n));isprime(sum(i=1,#v,v[i]*10^(#v-i)))
%o is(n)=ispolygonal(n,3)&&isA036952(n)
%o select(isA036952,vector(10^3,i,i*(i+1)/2)) \\ _Charles R Greathouse IV_, Jun 28 2013
%Y Intersection of A036952 and A000217.
%K nonn,base,less
%O 1,1
%A _K. D. Bajpai_, Jun 27 2013
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