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.

468, 4842, 27225, 235890, 21030930, 840827745

Offset: 1

Author

Paolo P. Lava, Feb 16 2017

Keywords

• nonn
• base
• more

Comments

Similar to rare numbers A035519.

No more terms < 10^12. - Lars Blomberg, Jul 12 2017

a(7), if it exists, is larger than 2*10^15. - Giovanni Resta, Jul 14 2017

Examples

			(468 - 1/2*864)^(1/2) = (36)^(1/2) = 6  and (468 +1/2*864)^(1/2) = (900)^(1/2) = 30.
		

Crossrefs

Cf. A004086, A035519.

Programs

Maple

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:=proc(q,k) local n; for n from 1 to q do
if n>k*R(n) then if frac(sqrt(n-k*R(n)))=0 and frac(sqrt(n+k*R(n)))=0
then print(n); fi; fi; od; end: P(10^9,1/2);

Extensions

a(6) from Lars Blomberg, Jul 12 2017