A194374
Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=sqrt(5) and < > denotes fractional part.
4, 8, 12, 16, 72, 76, 80, 84, 88, 144, 148, 152, 156, 160, 216, 220, 224, 228, 232, 288, 292, 296, 300, 304, 1292, 1296, 1300, 1304, 1308, 1364, 1368, 1372, 1376, 1380, 1436, 1440, 1444, 1448, 1452, 1508, 1512, 1516, 1520, 1524, 1580, 1584, 1588, 1592, 1596, 2584, 2588, 2592, 2596
Offset: 1
Keywords
Programs
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Mathematica
r = Sqrt[5]; c = 1/2; 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, 100}]; Flatten[Position[t1, 1]] (* empty *) t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}]; Flatten[Position[t2, 1]] (* A194374 *) t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}]; Flatten[Position[t3, 1]] (* A194375 *) -
PARI
isok(m) = my(r=sqrt(5)); sum(k=1, m, frac(1/2+k*r)-frac(k*r)) == 0; \\ Michel Marcus, Jan 31 2023
Extensions
More terms from Michel Marcus, Jan 31 2023
Comments