A295188 Decimal expansion of phi^3 * exp(1 - 1/phi), where phi is the golden ratio.

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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Index entries for transcendental numbers

Formula

Equals ((1+sqrt(5))/2)^3 * exp(1 - 2/(1+sqrt(5))).

Equals limit n->infinity (A066399(n)/n!)^(1/n).

Equals limit n->infinity (A239761(n)/n!)^(1/n).

Equals limit n->infinity (A295183(n)/n!)^(1/n).

Example

6.206527038397163731000740532186580585278052870847962022926...

Maple

evalf(((1+sqrt(5))/2)^3 * exp(1 - 2/(1+sqrt(5))), 120);

Mathematica

RealDigits[GoldenRatio^3 * Exp[1 - 1/GoldenRatio], 10, 110][[1]]

Prog

(PARI) phi=(sqrt(5)+1)/2; phi^3*exp(2-phi) \\ Charles R Greathouse IV, Nov 21 2024

Crossrefs

Cf. A001622, A066399, A239761, A295183.

Sequence in context: A154480 A087199 A153735 * A248680 A021621 A197844

Adjacent sequences: A295185 A295186 A295187 * A295189 A295190 A295191

Keyword

nonn,cons

Author

Vaclav Kotesovec, Nov 16 2017

Status

approved