A344388 Decimal expansion of a constant related to the asymptotics of A048634.

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

Offset: 1

Author

Vaclav Kotesovec, Aug 16 2021

Keywords

• nonn
• cons

Comments

This constant is a very close to A201506.

Conjecture: It is equal to the limit of column "h^2" in the Table 1 in reference by Wright and Trefethen, p. 336.

Examples

			1.05747359610293071458836136901117212325956834040149469519600889340841418929257...
		

Links

• T. G. Wright and L. N. Trefethen, Computed Lyapunov constants for random recurrences with smooth coefficients, J. Comp. Appl. Math. 132 (2) (2001), 331-340, Table 1.

Crossrefs

Cf. A048634, A092526, A201506.

Programs

Mathematica

A092526 = 1/3 + 2/(3*(116 + 12*Sqrt[93])^(1/3)) + (1/6)*(116 + 12*Sqrt[93])^(1/3); terms = 500; b = ConstantArray[0, terms]; b[[7]] = N[Log[2], 1000]; b[[8]] = N[Log[3], 1000]; b[[9]] = N[Log[5], 1000]; Quiet[Do[b[[n]] = b[[n-1]] + b[[n-3]] - Sum[Exp[k*(b[[n-2]] - b[[n-1]] - b[[n-3]])]/k*(-1)^k, {k, 1, 1000}], {n, 10, terms}]; Exp[Table[N[b[[n]]/A092526^n, 110], {n, Length[b] - 20, Length[b]}]]]

Formula

Equals exp(limit_{n->infinity} log(A048634(n)) / A092526^n ).