A273180 Numbers n such that ror(n) + rol(n) is a power of 2, where ror(n)=A038572(n) is n rotated one binary place to the right, rol(n)=A006257(n) is n rotated one binary place to the left.

1, 2, 6, 19, 38, 102, 307, 614, 1638, 4915, 9830, 26214, 78643, 157286, 419430, 1258291, 2516582, 6710886, 20132659, 40265318, 107374182, 322122547, 644245094, 1717986918, 5153960755, 10307921510, 27487790694, 82463372083, 164926744166, 439804651110

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,17,0,0,-16).

Formula

From Colin Barker, May 19 2016: (Start)

a(n) = 17*a(n-3) - 16*a(n-6) for n>6.

G.f.: x*(1+2*x+6*x^2+2*x^3+4*x^4) / ((1-x)*(1+x+x^2)*(1-16*x^3)).

(End)

Mathematica

Select[Range[10^6], IntegerQ@ Log2[FromDigits[RotateRight@ #, 2] + FromDigits[RotateLeft@ #, 2]] &@ IntegerDigits[#, 2] &] (* or *)
Rest@ CoefficientList[Series[x (1 + 2 x + 6 x^2 + 2 x^3 + 4 x^4)/((1 - x) (1 + x + x^2) (1 - 16 x^3)), {x, 0, 30}], x] (* Michael De Vlieger, May 19 2016 *)

Prog

(C)
#include <stdio.h>
int main(int argc, char** argv)
{
  unsigned long long x, n, BL=0;
  for (n=1; n>0; ++n) {
    if ((n & (n-1))==0)  ++BL;
    x = (n>>1) + ((n&1) << (BL-1));   // A038572(n)
    x+= (n*2) - (1ull<<BL) + 1;   // A006257(n)  for n>0
    if ((x & (x-1))==0)  printf("%lld, ", n);
  }
}
(PARI) Vec(x*(1+2*x+6*x^2+2*x^3+4*x^4)/((1-x)*(1+x+x^2)*(1-16*x^3)) + O(x^50)) \\ Colin Barker, May 19 2016

Crossrefs

Cf. A006257, A038572, A088161, A088163, A112627, A273105, A273106.

Sequence in context: A186769 A213400 A282080 * A280041 A058081 A192709

Adjacent sequences: A273177 A273178 A273179 * A273181 A273182 A273183

Keyword

nonn,base,easy

Author

Alex Ratushnyak, May 17 2016

Status

approved