A257296 Arithmetic mean of the digits of n, multiplied by 10^(d-1) and rounded down, where d is the number of digits of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 30, 35, 40, 45, 50, 55, 60, 65

Offset

0,3

Comments

The reason for the factor 10^(d-1) in the definition is to produce an analog of A257294, i.e., give the first d digits of the mean value, for an "average" d-digit number. But since the arithmetic mean of the digits may be between 0 and 1, the situation is slightly different from the case of the geometric mean.

Also motivated by sequence A257829.

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Formula

a(n) = floor(A007953(n)/A055642(n)*10^(A055642(n)-1))

Example

For n = 12, a two-digit number, the average of the digits is 1.50000..., so a(12) = 15.

Maple

f:= proc(n) local d;
     d:= ilog10(n);
     floor(convert(convert(n, base, 10), `+`)/(d+1)*10^d)
end proc:
map(f, [$0..100]); # Robert Israel, May 10 2015

Mathematica

Table[Floor[Mean[IntegerDigits[n]]10^(IntegerLength[n]-1)], {n, 0, 70}] (* Harvey P. Dale, Mar 11 2020 *)

Prog

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

Crossrefs

Cf. A004426, A004427, A007953, A055642, A257829.

Sequence in context: A081596 A061500 A051796 * A093030 A122425 A360073

Adjacent sequences: A257293 A257294 A257295 * A257297 A257298 A257299

Keyword

nonn,base,easy,look

Author

M. F. Hasler, May 10 2015

Status

approved