A202475 Decimal expansion of the real number x between 3 and 4 where 2^x = x!.

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

Offset: 1

Author

Colm Mulcahy, Dec 19 2011

Keywords

• nonn
• cons

Comments

2^3 > 3! but 2^4 < 4!. Since the exponential and generalized factorial (Gamma) functions are continuous, it follows that 2^x = x! ( = gamma(x+1) ) for some x between 3 and 4. It's about 3.45986564404500.

Examples

			3.459865644044999134187861081068981202775184599...
		

Links

• WolframAlpha, Find value

Programs

Mathematica

RealDigits[x/.FindRoot[2^x==x!,{x,3,4},WorkingPrecision->120]][[1]] (* Harvey P. Dale, Jan 22 2016 *)

PARI

solve(x=3, 4, 2^x-gamma(x+1)) \\ Michel Marcus, Aug 03 2013

Extensions

More terms from D. S. McNeil, Dec 19 2011