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

0,3

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.

Links

Table of n, a(n) for n=0..76.

Formula

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

Example

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

Prog

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

Crossrefs

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

Sequence in context: A088117 A349278 A195833 * A330970 A139281 A059707

Adjacent sequences: A257291 A257292 A257293 * A257295 A257296 A257297

Keyword

nonn,base

Author

M. F. Hasler, May 10 2015

Status

approved