A085060 Integer reached in A085058.

3, 12, 12, 39, 21, 39, 30, 120, 39, 66, 48, 120, 57, 93, 66, 363, 75, 120, 84, 201, 93, 147, 102, 363, 111, 174, 120, 282, 129, 201, 138, 1092, 147, 228, 156, 363, 165, 255, 174, 606, 183, 282, 192, 444, 201, 309, 210, 1092, 219, 336, 228, 525, 237, 363, 246, 849, 255, 390

Offset

0,1

Links

Ruud H.G. van Tol, Table of n, a(n) for n = 0..10000

J. C. Lagarias and N. J. A. Sloane, Approximate Squaring, Experimental Math., 13 (2004), 113-128; alternative link; pdf, ps.

Formula

n << a(n) << n^1.6. (The actual upper exponent is log(3)/log(2) = 1.5849625....) - Charles R Greathouse IV, Aug 29 2024

From Ruud H.G. van Tol, Aug 31 2024: (Start)

a(2*n) = 9*n + 3.

a(2*n+1) = 3*a(n) + 3.

a(n) = (3/2)^A085058(n) * (2*n+2) - 3/2. (End)

Sum_{k=1..n} a(k) ~ 9*n^2/2. - Amiram Eldar, Apr 04 2026

Mathematica

a[n_] := (3/2)^IntegerExponent[2*n+2, 2]*(3*n+3) - 3/2; Array[a, 60, 0] (* Amiram Eldar, Apr 04 2026 *)

Prog

(PARI) a(n) = (3/2)^valuation(2*n+2, 2)*(3*n+3)-3/2; \\ Ruud H.G. van Tol, Aug 29 2024
(Python)
def A085060(n): return (3*(k:=n+1)*3**(m:=(-k&k).bit_length())>>m)-1 # Chai Wah Wu, Feb 26 2025

Crossrefs

Cf. A020857, A085058, A085062.

Sequence in context: A292624 A192788 A336276 * A340354 A263672 A233287

Adjacent sequences: A085057 A085058 A085059 * A085061 A085062 A085063

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 11 2003

Status

approved