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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.
1
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.
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
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, May 10 2015
STATUS
approved