A257294 The first d decimal digits of the geometric mean of the digits of n, where d is the number of digits of n, without leading zeros.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 10, 14, 17, 20, 22, 24, 26, 28, 30, 0, 14, 20, 24, 28, 31, 34, 37, 40, 42, 0, 17, 24, 30, 34, 38, 42, 45, 48, 51, 0, 20, 28, 34, 40, 44, 48, 52, 56, 60, 0, 22, 31, 38, 44, 50, 54, 59, 63, 67, 0, 24, 34, 42, 48, 54, 60, 64, 69, 73, 0, 26, 37, 45, 52, 59, 64

Offset: 0

Author

M. F. Hasler, May 10 2015

Keywords

• nonn
• base

Comments

Since the geometric mean of the digits of any number is either 0 or between 1 and 9, "the first d digits" is equivalent to the integer part of this value multiplied by 10^(d-1), which leads to the given formula.

Motivated by sequence A257830.

Examples

			For n = 11, a 2-digit number, the geometric mean of the digits is trivially 1, which is 1.000..., and the first two decimal digits are 10, so a(11) = 10. For n=12, geometric mean is sqrt(2) = 1.414..., so a(12) = 14. - _N. J. A. Sloane_, May 11 2015
		

Crossrefs

Cf. A004428, A004429, A007954, A055642, A257830.

Programs

PARI

a(n)=sqrtn(prod(i=1, #n=digits(n), n[i]), #n)\10^(1-#n)

Formula

a(n) = floor(A007954(n)^(1/A055642(n))*10^(A055642(n)-1))