A194414
Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - ) > 0, where r=sqrt(2) and < > denotes fractional part.
1, 4, 5, 6, 7, 8, 10, 11, 13, 16, 17, 18, 19, 20, 22, 23, 25, 28, 29, 30, 31, 32, 34, 35, 37, 40, 46, 47, 49, 52, 58, 59, 61, 64, 76, 88, 100, 103, 104, 105, 106, 107, 109, 110, 112, 115, 116, 117, 118, 119, 121, 122, 124, 127, 128, 129, 130, 131, 133, 134
Offset: 1
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 1..5000
Programs
-
Mathematica
r = Sqrt[2]; c = 1/3; x[n_] := Sum[FractionalPart[k*r], {k, 1, n}] y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}] t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}]; Flatten[Position[t1, 1]] (* A194411 *) t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}]; Flatten[Position[t2, 1]] (* A194412 *) %/3 (* A194413 *) t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 150}]; Flatten[Position[t3, 1]] (* A194414 *)
Comments