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

Author

N. J. A. Sloane, Aug 11 2003

Keywords

• nonn
• easy

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 (pdf, ps), Experimental Math., 13 (2004), 113-128.

Crossrefs

Cf. A085058, A085062.

Programs

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

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)