cp's OEIS Frontend

A274524 Numbers n such that both ror(n) and rol(n) are squares, where ror(x)=A038572(x) is x rotated one binary place to the right, rol(x)=A006257(x) is x rotated one binary place to the left.

%I A274524 #11 Jul 14 2016 00:18:57
%S A274524 1,2,8,32,128,512,1568,2048,2312,2592,2888,8192,16928,32768,131072,
%T A274524 139392,250632,524288,549152,566048,672800,924800,963272,1318688,
%U A274524 2097152,8388608,8520192,8769672,9005768,12261152,13582472,15635232,33554432,134217728,136059008,136587392
%N A274524 Numbers n such that both ror(n) and rol(n) are squares, where ror(x)=A038572(x) is x rotated one binary place to the right, rol(x)=A006257(x) is x rotated one binary place to the left.
%C A274524 A004171 and A081294 are subsequences.
%C A274524 From _Robert Israel_, Jul 13 2016: (Start)
%C A274524 All terms except 1 are even.
%C A274524 Even terms are the numbers of the form n = (a+b)^2/8 such that for some d >= 1,
%C A274524 2^d <= n < 2^(d+1) and 2^(d+1)-1 = a*b. (End)
%H A274524 Robert Israel, <a href="/A274524/b274524.txt">Table of n, a(n) for n = 1..10000</a>
%p A274524 F:= proc(d) local v,R,X;
%p A274524       v:= 2^(d+1)-1;
%p A274524       R:= select(t-> t^2 < v,numtheory:-divisors(v));
%p A274524       op(select(t -> t >= (v+1)/2 and t < v+1, map(t -> (t+ v/t)^2/8, R)));
%p A274524 end proc:
%p A274524 sort(convert({1,seq(F(i),i=1..50)},list)); # _Robert Israel_, Jul 13 2016
%t A274524 Select[Range[10^6], Times @ Boole@ {IntegerQ@ Sqrt@ FromDigits[RotateRight@ #, 2], IntegerQ@ Sqrt@ FromDigits[RotateLeft@ #, 2]} &@ IntegerDigits[#, 2] == 1 &] (* _Michael De Vlieger_, Jun 29 2016 *)
%Y A274524 Cf. A006257, A038572, A004171, A081294.
%K A274524 nonn,base
%O A274524 1,2
%A A274524 _Alex Ratushnyak_, Jun 27 2016