A297701 Decimal expansion of 1 + sqrt(2) + sqrt(3).

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

Offset: 1

Author

Alonso del Arte, Jan 03 2018

Keywords

• nonn
• cons
• easy

Comments

This is an algebraic integer of degree 4, with minimal polynomial x^4 - 4*x^3 - 4*x^2 + 16*x - 8.

Examples

			  1.0000000000000000000000000000...
+ 1.4142135623730950488016887242...
+ 1.7320508075688772935274463415...
= 4.1462643699419723423291350657...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Index entries for algebraic numbers, degree 4

Crossrefs

Essentially the same as A135611. Cf. A002193, A002194, A014176, A165663, A188582.

Programs

Magma

SetDefaultRealField(RealField(100)); 1 + Sqrt(2) + Sqrt(3); // G. C. Greubel, Nov 20 2018

Mathematica

RealDigits[1 + Sqrt[2] + Sqrt[3], 10, 100][[1]]

PARI

1+sqrt(2)+sqrt(3) \\ Felix Fröhlich, Jan 06 2018

Sage

numerical_approx(1+sqrt(2)+sqrt(3), digits=100) # G. C. Greubel, Nov 20 2018

Formula

1 + sqrt(2) + sqrt(3) = 1 + sqrt(5 + 2 sqrt(6)).

1 + A002193 + A002194 = A014176 + A002194 = A165663 + A188582. - Felix Fröhlich, Jan 06 2018

Extensions

Terms a(52) onward corrected by G. C. Greubel, Nov 20 2018