A375820 Decimal expansion of 333/106.

3, 1, 4, 1, 5, 0, 9, 4, 3, 3, 9, 6, 2, 2, 6, 4, 1, 5, 0, 9, 4, 3, 3, 9, 6, 2, 2, 6, 4, 1, 5, 0, 9, 4, 3, 3, 9, 6, 2, 2, 6, 4, 1, 5, 0, 9, 4, 3, 3, 9, 6, 2, 2, 6, 4, 1, 5, 0, 9, 4, 3, 3, 9, 6, 2, 2, 6, 4, 1, 5, 0, 9, 4, 3, 3, 9, 6, 2, 2, 6, 4, 1, 5, 0, 9, 4, 3, 3, 9, 6, 2, 2, 6, 4, 1, 5, 0, 9, 4, 3

Offset: 1

Author

Stefano Spezia, Aug 30 2024

Keywords

• nonn
• cons
• easy

Comments

Approximation of Pi accurate up to five digits.

Periodic of period [4, 1, 5, 0, 9, 4, 3, 3, 9, 6, 2, 2, 6] of length 13.

Examples

			3.1415094339622641509433962264150943396226415...
		

References

• Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 154-155.
• David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 49.

Links

• Michael A. B. Deakin and H. Lausch, The Bible and Pi, The Mathematical Gazette, 82(494), 162-166 (1998).
• Wikipedia, Adriaan Metius.
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A000796, A068079, A210622.

Programs

Mathematica

RealDigits[333/106,10,100][[1]]

Python

def A375820(n): return (2, 2 ,6, 4, 1, 5, 0, 9, 4, 3, 3, 9, 6)[n%13] if n>2 else 5-(n<<1) # Chai Wah Wu, Aug 30 2024

Formula

Equals (2*355 - 377)/(2*113 - 120), where A068079 = 355/113 and A210622 = 377/120 [Adriaen Metius]. See Wells.