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
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).
Programs
-
C
#include
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< -
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 *) -
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
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)