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.

1, 2, 8, 32, 128, 512, 1568, 2048, 2312, 2592, 2888, 8192, 16928, 32768, 131072, 139392, 250632, 524288, 549152, 566048, 672800, 924800, 963272, 1318688, 2097152, 8388608, 8520192, 8769672, 9005768, 12261152, 13582472, 15635232, 33554432, 134217728, 136059008, 136587392

Offset: 1

Author

Alex Ratushnyak, Jun 27 2016

Keywords

• nonn
• base

Comments

A004171 and A081294 are subsequences.

From Robert Israel, Jul 13 2016: (Start)

All terms except 1 are even.

Even terms are the numbers of the form n = (a+b)^2/8 such that for some d >= 1,

2^d <= n < 2^(d+1) and 2^(d+1)-1 = a*b. (End)

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006257, A038572, A004171, A081294.

Programs

Maple

F:= proc(d) local v,R,X;
      v:= 2^(d+1)-1;
      R:= select(t-> t^2 < v,numtheory:-divisors(v));
      op(select(t -> t >= (v+1)/2 and t < v+1, map(t -> (t+ v/t)^2/8, R)));
end proc:
sort(convert({1,seq(F(i),i=1..50)},list)); # Robert Israel, Jul 13 2016

Mathematica

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 *)