A375743 -id:A375743 - cp's OEIS frontend

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

Stefano Spezia, Jul 24 2025

Baudhayana used the fraction 577/408 to approximate sqrt(2) (see Tattersall).
Periodic of period 16.
8th convergent of sqrt(2).

			1.414215686274509803921568627450980392156862745...

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

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).

Cf. A000129, A001333, A002193, A375743.

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

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).

cp's OEIS Frontend

A386523 Decimal expansion of 577/408.

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