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

Author

Vaclav Kotesovec, Nov 16 2017

Keywords

• nonn
• cons

Examples

			6.206527038397163731000740532186580585278052870847962022926...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A001622, A066399, A239761, A295183.

Programs

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]]

PARI

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

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).