

A322258


Decimal expansion of exp(phi/sqrt(5)), where phi is the golden ratio.


1



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

0,1


REFERENCES

J. Sandor and B. Crstici, Handbook of Number Theory II, Springer, 2004, pp. 5455, p. 182.


LINKS



FORMULA

Equals Product_{k>=1} (L(k)/(sqrt(5)*F(k)))^(phi(k)/k), where L(k) and F(k) are the Lucas and Fibonacci numbers, and phi(k) is the Euler totient function.


EXAMPLE

0.48499980129295802523175132230095248348065996564155...


MATHEMATICA

RealDigits[Exp[GoldenRatio/Sqrt[5]], 10, 120][[1]]


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



