A392289 - OEIS

%I #9 May 19 2026 22:30:35

%S 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,

%T 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,

%U 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

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

%C 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.

%H Shifa Liu, <a href="https://doi.org/10.33774/coe-2025-k5pls">Threefold Precise Patterns in Quark Mass Algebra: A Unified Link to Leptons and Nucleons</a>, Cambridge Open Engage (2025).

%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.

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

%e 0.420861431432846676750756803854278151370703838...

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

%o (PARI) sqrt((3-sqrt(7))/2) \\ _Charles R Greathouse IV_, May 19 2026

%Y Cf. A010465, A392290 (other parameter).

%K nonn,cons,easy

%O 0,1

%A _Stefano Spezia_, Jan 06 2026