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A194406 Numbers m such that Sum_{k=1..m} (<1/2 + k*e> - <k*e>) = 0 where < > denotes fractional part. 4
2, 4, 6, 8, 12, 26, 30, 32, 34, 36, 38, 40, 44, 58, 62, 64, 66, 68, 70, 74, 78, 80, 82, 84, 86, 90, 94, 96, 98, 100, 102, 106, 110, 112, 114, 116, 118, 122, 126, 128, 130, 132, 134, 138, 152, 156, 158, 160, 162, 164, 166, 170, 184, 188, 190, 192, 194, 196 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Every term is even; see A194368.

LINKS

Table of n, a(n) for n=1..58.

MATHEMATICA

r = E; 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, 200}];

Flatten[Position[t1, 1]]       (* A194405 *)

t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];

Flatten[Position[t2, 1]]       (* A194406 *)

t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];

Flatten[Position[t3, 1]]       (* A194407 *)

CROSSREFS

Cf. A194368.

Sequence in context: A001217 A131885 A173941 * A087443 A036035 A063008

Adjacent sequences:  A194403 A194404 A194405 * A194407 A194408 A194409

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 24 2011

STATUS

approved

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Last modified January 27 10:39 EST 2022. Contains 350607 sequences. (Running on oeis4.)