A004426 -id:A004426 - cp's OEIS frontend

A074464 Average digit (rounded down) in the decimal expansion of a prime number p, where 2^p-1 is a Mersenne prime.

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

Offset: 1

Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 23 2002

			Prime numbers for Mersenne are 2, 3, 5, 7, 13, 17, 19, 31, 61, ..., so the averages of digits rounded down are 2, 3, 5, 7, (1+3)/2 = 2, (1+7)/2 = 4, (1+9)/2 = 5, (3+1)/2 = 2, floor((6+1)/2) = 3, ...

Cf. A000043, A004426, A074463.

Floor[Mean[IntegerDigits[#]]]&/@MersennePrimeExponent[Range[47]] (* Harvey P. Dale, Apr 19 2019 *)

a(n) = A004426(A000043(n)). - Michel Marcus, Aug 04 2018

a(21)-a(47) from Ivan Panchenko, Aug 03 2018

a(48) from Amiram Eldar, Oct 16 2024

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.

Original entry on oeis.org

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

M. F. Hasler, May 10 2015

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.

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

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

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

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

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

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

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

A285093 Corresponding values of arithmetic means of digits of numbers from A061383.

Original entry on oeis.org

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

Offset: 0

Jaroslav Krizek, Apr 14 2017

Jaroslav Krizek, Table of n, a(n) for n = 0..3000

Cf. A061383 (numbers with integer arithmetic mean of digits in base 10).
Sequences of numbers n such that a(n) = k for k = 1 - 9: A061384 (k = 1), A061385 (k = 2), A061386 (k = 3), A061387 (k = 4), A061388 (k = 5), A061423 (k = 6), A061424 (k = 7), A061425 (k = 8), A002283 (k = 9).
Cf. A004426, A004427, A257295 (supersequences).

[0] cat [&+Intseq(n) / #Intseq(n): n in [1..100000] | &+Intseq(n) mod #Intseq(n) eq 0];

lista(nn) = {for (n=0, nn, if (n, d = digits(n), d = [0]); if (!( vecsum(d) % #d), print1(vecsum(d)/#d, ", ")););} \\ Michel Marcus, Apr 15 2017

a(n) = A007953(A061383(n)) / A055642(A061383(n)) for n >= 1.

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A074464 Average digit (rounded down) in the decimal expansion of a prime number p, where 2^p-1 is a Mersenne prime.

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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.

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A285093 Corresponding values of arithmetic means of digits of numbers from A061383.

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