A396822 Decimal expansion of (4711 + 3*sqrt(7))/1736.

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

Offset

1,1

Comments

An approximation for e, accurate to 9 decimal places, constructed geometrically by Sandham (1947).

References

Roy Dubisch, The Teaching of Mathematics: From Intermediate Algebra through First Year Calculus, John Wiley and Sons, Inc., 1975, p. 87.

Links

Table of n, a(n) for n=1..105.

Karel Drábek, K přibližné konstrukci čísla e (in Czech), Rozhledy Matematicko Fyzikální, Vol. 47 (1968-69), pp. 274-276.

H. F. Sandham, An Approximate Construction for e, The American Mathematical Monthly, Vol. 54, No. 4 (1947), pp. 215-216.

Eric Weisstein's World of Mathematics, e Approximations.

Index entries for algebraic numbers, degree 2.

Formula

Equals (228 + 11*sqrt(7))/(84 + 4*sqrt(7)).

Equals e - 1.565...*10^(-10).

Minimal polynomial: 6944*x^2 - 37688*x + 51137.

Example

2.718281828302530974522756248422187662025996991675833...

Mathematica

RealDigits[(4711 + 3*Sqrt[7])/1736, 10, 120][[1]]

Prog

(PARI) (4711 + 3*sqrt(7))/1736

Crossrefs

Cf. A001113 (e), A060302, A368617, A368653, A368656.

Sequence in context: A368617 A060302 A368656 * A001113 A368653 A248685

Adjacent sequences: A396819 A396820 A396821 * A396823 A396826 A396827

Keyword

nonn,cons

Author

Amiram Eldar, Jun 07 2026

Status

approved