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A344388
Decimal expansion of a constant related to the asymptotics of A048634.
2
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
1,3
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.
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.
FORMULA
Equals exp(limit_{n->infinity} log(A048634(n)) / A092526^n ).
EXAMPLE
1.05747359610293071458836136901117212325956834040149469519600889340841418929257...
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]}]]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Aug 16 2021
STATUS
approved