A385177 a(n) = Sum_{k=1..n} ceiling(k/phi), where phi is the golden ratio (A001622).

1, 3, 5, 8, 12, 16, 21, 26, 32, 39, 46, 54, 63, 72, 82, 92, 103, 115, 127, 140, 153, 167, 182, 197, 213, 230, 247, 265, 283, 302, 322, 342, 363, 385, 407, 430, 453, 477, 502, 527, 553, 579, 606, 634, 662, 691, 721, 751, 782, 813, 845, 878, 911, 945, 979, 1014, 1050, 1086, 1123

Offset

1,2

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Formula

a(n) = A183136(n) + n.

Mathematica

Accumulate[Ceiling[Range[100]/GoldenRatio]]

Prog

(Python)
from math import isqrt
def A385177(n): return n+sum(isqrt(5*i**2)-i>>1 for i in range(1, n+1)) # Chai Wah Wu, Jun 20 2025

Crossrefs

Cf. A001622, A183136.

Partial sums of A019446.

Sequence in context: A236538 A194176 A186494 * A371702 A194180 A000212

Adjacent sequences: A385174 A385175 A385176 * A385178 A385179 A385180

Keyword

nonn,easy

Author

Paolo Xausa, Jun 20 2025

Status

approved