A392502 Decimal expansion of the absolute value of the second smallest real root of the minimal polynomial of Conway's constant.

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

Offset

1,6

Comments

The minimal polynomial of Conway's constant has three real roots, -A392501, minus this constant and Conway's constant A014715.

Links

Table of n, a(n) for n=1..78.

Eric Weisstein's World of Mathematics, Conway's Constant.

Index entries for algebraic numbers, degree 71.

Formula

x = -this satisfies x^71 - x^69 - 2*x^68 - x^67 + 2*x^66 + 2*x^65 + x^64 - x^63 - x^62 - x^61 - x^60 - x^59 + 2*x^58 + 5*x^57 + 3*x^56 - 2*x^55 - 10*x^54 - 3*x^53 - 2*x^52 + 6*x^51 + 6*x^50 + x^49 + 9*x^48 - 3*x^47 - 7*x^46 - 8*x^45 - 8*x^44 + 10*x^43 + 6*x^42 + 8*x^41 - 5*x^40 - 12*x^39 + 7*x^38 - 7*x^37 + 7*x^36 + x^35 - 3*x^34 + 10*x^33 + x^32 - 6*x^31 - 2*x^30 - 10*x^29 - 3*x^28 + 2*x^27 + 9*x^26 - 3*x^25 + 14*x^24 - 8*x^23 - 7*x^21 + 9*x^20 + 3*x^19 - 4*x^18 - 10*x^17 - 7*x^16 + 12*x^15 + 7*x^14 + 2*x^13 - 12*x^12 - 4*x^11 - 2*x^10 + 5*x^9 + x^7 - 7*x^6 + 7*x^5 - 4*x^4 + 12*x^3 - 6*x^2 + 3*x - 6 = 0.

Example

1.0111538201012584804076933993593740625752...

Mathematica

RealDigits[x /. Solve[x^71 - x^69 - 2*x^68 - x^67 + 2*x^66 + 2*x^65 + x^64 - x^63 - x^62 - x^61 - x^60 - x^59 + 2*x^58 + 5*x^57 + 3*x^56 - 2*x^55 - 10*x^54 - 3*x^53 - 2*x^52 + 6*x^51 + 6*x^50 + x^49 + 9*x^48 - 3*x^47 - 7*x^46 - 8*x^45 - 8*x^44 + 10*x^43 + 6*x^42 + 8*x^41 - 5*x^40 - 12*x^39 + 7*x^38 - 7*x^37 + 7*x^36 + x^35 - 3*x^34 + 10*x^33 + x^32 - 6*x^31 - 2*x^30 - 10*x^29 - 3*x^28 + 2*x^27 + 9*x^26 - 3*x^25 + 14*x^24 - 8*x^23 - 7*x^21 + 9*x^20 + 3*x^19 - 4*x^18 - 10*x^17 - 7*x^16 + 12*x^15 + 7*x^14 + 2*x^13 - 12*x^12 - 4*x^11 - 2*x^10 + 5*x^9 + x^7 - 7*x^6 + 7*x^5 - 4*x^4 + 12*x^3 - 6*x^2 + 3*x - 6 == 0][[2]], 10, 100][[1]] (* Vaclav Kotesovec, Jan 16 2026 *)

Prog

(PARI) -polrootsreal(Pol([1, 0, -1, -2, -1, 2, 2, 1, -1, -1, -1, -1, -1, 2, 5, 3, -2, -10, -3, -2, 6, 6, 1, 9, -3, -7, -8, -8, 10, 6, 8, -5, -12, 7, -7, 7, 1, -3, 10, 1, -6, -2, -10, -3, 2, 9, -3, 14, -8, 0, -7, 9, 3, -4, -10, -7, 12, 7, 2, -12, -4, -2, 5, 0, 1, -7, 7, -4, 12, -6, 3, -6]))[2]

Crossrefs

Cf. A014715, A392501.

Sequence in context: A018222 A349578 A388333 * A374260 A305921 A241149

Adjacent sequences: A392499 A392500 A392501 * A392503 A392504 A392505

Keyword

nonn,cons

Author

A.H.M. Smeets, Jan 14 2026

Status

approved