cp's OEIS Frontend

A282116 Numbers k such that k-1/2*R(k) and k+1/2*R(k) are both positive squares, where R(k) is the digits reverse of k.

%I A282116 #15 Jul 14 2017 04:20:45
%S A282116 468,4842,27225,235890,21030930,840827745
%N A282116 Numbers k such that k-1/2*R(k) and k+1/2*R(k) are both positive squares, where R(k) is the digits reverse of k.
%C A282116 Similar to rare numbers A035519.
%C A282116 No more terms < 10^12. - _Lars Blomberg_, Jul 12 2017
%C A282116 a(7), if it exists, is larger than 2*10^15. - _Giovanni Resta_, Jul 14 2017
%e A282116 (468 - 1/2*864)^(1/2) = (36)^(1/2) = 6  and (468 +1/2*864)^(1/2) = (900)^(1/2) = 30.
%p A282116 R:=proc(w) local x,y,z; x:=w; y:=0; for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10); od; y; end:
%p A282116 P:=proc(q,k) local n; for n from 1 to q do
%p A282116 if n>k*R(n) then if frac(sqrt(n-k*R(n)))=0 and frac(sqrt(n+k*R(n)))=0
%p A282116 then print(n); fi; fi; od; end: P(10^9,1/2);
%Y A282116 Cf. A004086, A035519.
%K A282116 nonn,base,more
%O A282116 1,1
%A A282116 _Paolo P. Lava_, Feb 16 2017
%E A282116 a(6) from _Lars Blomberg_, Jul 12 2017