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A350526 a(n) = f(n*r)*c(n/r), where f = floor, c = ceiling, and r = golden ratio (A001622). 2
1, 6, 8, 18, 32, 36, 55, 60, 84, 112, 119, 152, 189, 198, 240, 250, 297, 348, 360, 416, 429, 490, 555, 570, 640, 714, 731, 810, 828, 912, 1000, 1020, 1113, 1210, 1232, 1334, 1357, 1464, 1575, 1600, 1716, 1742, 1863, 1988, 2016, 2146, 2280, 2310, 2449, 2480 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The golden ratio r is the unique number x such that f(n*x)*c(n/x) - c(n*x)f(n/x) = n for all n >= 1.

LINKS

Table of n, a(n) for n=1..50.

FORMULA

a(n) = n + A350527(n) = n + c(n*r)*f(n/r), where f = floor, c = ceiling, and r = golden ratio.

MATHEMATICA

r = GoldenRatio; c[x_] := Ceiling[x]; f[x_] := Floor[x];

Table[f[n r]*c[n/r], {n, 1, 100}] (* A350526 *)

Table[c[n r]*f[n/r], {n, 1, 100}] (* A350527 *)

Table[f[n r]*c[n/r] - c[n r]*f[n/r], {n, 1, 100}] (* A000027 *)

CROSSREFS

Cf. A001622, A350527.

Sequence in context: A315945 A086913 A108341 * A173975 A349770 A349225

Adjacent sequences: A350523 A350524 A350525 * A350527 A350528 A350529

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 04 2022

STATUS

approved

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Last modified November 30 05:38 EST 2022. Contains 358431 sequences. (Running on oeis4.)