A386523 - OEIS

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

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OFFSET

1,2

COMMENTS

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

Periodic of period 16.

8th convergent of sqrt(2).

REFERENCES

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

LINKS

Table of n, a(n) for n=1..100.

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).

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).

EXAMPLE

1.414215686274509803921568627450980392156862745...

MATHEMATICA

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

CROSSREFS

Cf. A000129, A001333, A002193, A375743.

Sequence in context: A020807 A188582 A230077 * A055190 A155781 A161772

Adjacent sequences: A386520 A386521 A386522 * A386524 A386525 A386526

KEYWORD

nonn,cons,easy

AUTHOR

Stefano Spezia, Jul 24 2025

STATUS

approved