A392289 Decimal expansion of sqrt((3 - sqrt(7))/2).

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

Offset

0,1

Comments

This constant gives the value of one of the two parameters such that the up-type quark mass matrix has a realistic spectrum with hierarchical eigenvalues m_t >> m_c >> m_u where m_t, m_c, and m_u denote the masses of the three quark flavors t (top), c (charm), and u (up). See Liu's link on page 11.

Links

Table of n, a(n) for n=0..99.

Shifa Liu, Threefold Precise Patterns in Quark Mass Algebra: A Unified Link to Leptons and Nucleons, Cambridge Open Engage (2025).

Index entries for algebraic numbers, degree 4.

Formula

Minimal polynomial: 1 - 6*x^2 + 2*x^4.

Example

0.420861431432846676750756803854278151370703838...

Mathematica

RealDigits[Sqrt[(3-Sqrt[7])/2], 10, 100][[1]]

Prog

(PARI) sqrt((3-sqrt(7))/2) \\ Charles R Greathouse IV, May 19 2026

Crossrefs

Cf. A010465, A392290 (other parameter).

Sequence in context: A058546 A196774 A219245 * A299769 A091435 A330472

Adjacent sequences: A392286 A392287 A392288 * A392290 A392291 A392292

Keyword

nonn,cons,easy

Author

Stefano Spezia, Jan 06 2026

Status

approved