A386523 Decimal expansion of 577/408.

1, 4, 1, 4, 2, 1, 5, 6, 8, 6, 2, 7, 4, 5, 0, 9, 8, 0, 3, 9, 2, 1, 5, 6, 8, 6, 2, 7, 4, 5, 0, 9, 8, 0, 3, 9, 2, 1, 5, 6, 8, 6, 2, 7, 4, 5, 0, 9, 8, 0, 3, 9, 2, 1, 5, 6, 8, 6, 2, 7, 4, 5, 0, 9, 8, 0, 3, 9, 2, 1, 5, 6, 8, 6, 2, 7, 4, 5, 0, 9, 8, 0, 3, 9, 2, 1, 5, 6, 8, 6, 2, 7, 4, 5, 0, 9, 8, 0, 3, 9

Offset: 1

Author

Stefano Spezia, Jul 24 2025

Keywords

• nonn
• cons
• easy

Comments

Baudhayana used the fraction 577/408 to approximate sqrt(2) (see Tattersall).

Periodic of period 16.

8th convergent of sqrt(2).

Examples

			1.414215686274509803921568627450980392156862745...
		

References

• James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 257.

Links

• Wikipedia, Baudhayana.
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A000129, A001333, A002193, A375743.

Programs

Mathematica

RealDigits[577/408,10,100][[1]]

Formula

a(n) = a(n-16) for n > 20.

G.f.: (1 + 4*x + x^2 + 4*x^3 + 2*x^4 + x^5 + 5*x^6 + 6x^7 + 8*x^8 + 6*x^9 + 2*x^10 + 7*x^11 + 4*x^12 + 5*x^13 + 9*x^15 + 7*x^16 - 4*x^17 + 2*x^18 + 5*x^19)/(1 - x^16).

Equals A001333(8)/A000129(8).