A087478 Decimal expansion of (sqrt(20467) - sqrt(19578) + sqrt(10177) - sqrt(9553))/2.

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

Offset

1,1

Comments

This is the best approximation to Pi using four square roots (with coefficients +/-1) of n < 200000, see also A087477.

Links

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

Index entries for algebraic numbers, degree 16.

Formula

Minimal polynomial 65536*x^16 -7834828800*x^14 +325374898126848*x^12 -6225495726108876800*x^10 +57537829030165194290688*x^8 -232932990774015996420825600*x^6 +265705438949252749984375197376 *x^4 -2599773034587194227792227381600*x^2 +14994031012496054780625. - R. J. Mathar, Jun 03 2026

Example

3.14159265183290...

Mathematica

RealDigits[N[(Sqrt[20467] - Sqrt[19578] + Sqrt[10177] - Sqrt[9553])/2, 101]] (* Georg Fischer, Apr 03 2020 *)

Prog

(PARI) (sqrt(20467)-sqrt(19578)+sqrt(10177)-sqrt(9553))/2 \\ Charles R Greathouse IV, May 18 2026

Crossrefs

Cf. A000796, A087477.

Sequence in context: A013705 A358989 A216548 * A328927 A247385 A253214

Adjacent sequences: A087475 A087476 A087477 * A087479 A087480 A087481

Keyword

easy,nonn,cons

Author

Zak Seidov, Sep 09 2003

Extensions

a(100) corrected by Georg Fischer, Apr 03 2020

Status

approved