A004427 -id:A004427 - cp's OEIS frontend

A074462 Average digit (rounded up) in the decimal expansion of prime(n).

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

Offset: 1

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

			The prime numbers begin with 2,3,5,7,11,13,17,19,23,... so the average digits rounded up are 2, 3, 5, 7, (1+1)/2=1, (1+3)/2=2, (1+7)/2=4, (1+9)/2=5, ceiling((2+3)/2)=3, ...

Cf. A000040, A004427, A074461, A073342.

Cf. A007605, A097944.

Table[Ceiling[Mean[IntegerDigits[p]]],{p,Prime[Range[120]]}] (* Harvey P. Dale, Nov 06 2022 *)

a(n) = my(d=digits(prime(n))); ceil(vecsum(d)/#d); \\ Michel Marcus, Apr 23 2022

a(n) = ceiling(A007605(n)/A097944(n)). - R. J. Mathar, Sep 23 2008

a(n) = A004427(A000040(n)). - Reinhard Zumkeller, May 27 2010

Offset changed to 1, cf. to A073342 added, and extended by R. J. Mathar, Sep 23 2008

A178404 Numbers such that the rounded up arithmetic mean of their digits equals their digital root.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 99, 100, 149, 158, 167, 176, 185, 194, 239, 248, 257, 266, 275, 284, 293, 329, 338, 347, 356, 365, 374, 383, 392, 419, 428, 437, 446, 455, 464, 473, 482, 491, 509, 518, 527, 536, 545, 554, 563, 572, 581, 590, 608, 617, 626, 635

Offset: 1

Reinhard Zumkeller, May 27 2010

A004427(a(n)) = A010888(a(n)); complement of A178405.

			From _Reinhard Zumkeller_, May 28 2010: (Start)
1093 --> 1+0+9+3=13 --> A010888(1093) = 1+3 = 4 and also
1093 --> 1+0+9+3=13 --> A004427(1093) = ceiling(13/4) = 4,
therefore 1093 is a term: a(100) = 1093. (End)

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Cf. A004427, A010888, A178405.

A178404 := proc(n) option remember: local k: if(n=1)then return 0: fi: k:=procname(n-1)+1: do if(ceil(add(d, d=convert(k,base,10))/length(k))-1 = (k-1) mod 9)then return k: fi: k:=k+1: od: end: seq(A178404(n),n=1..57); # Nathaniel Johnston, May 04 2011

amdrQ[n_]:=NestWhile[Total[IntegerDigits[#]]&,n,#>9&]==Ceiling[ Mean[ IntegerDigits[n]]]; Select[Range[0,1000],amdrQ] (* Harvey P. Dale, Oct 10 2013 *)

A178405 Numbers such that the rounded up arithmetic mean of their digits differs from their digital root.

Original entry on oeis.org

11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76

Offset: 1

Reinhard Zumkeller, May 27 2010

A004427(a(n)) <> A010888(a(n)); complement of A178404.

R. Zumkeller, Table of n, a(n) for n = 1..10000

A180157 Arithmetic mean of digits is not an integer.

Original entry on oeis.org

10, 12, 14, 16, 18, 21, 23, 25, 27, 29, 30, 32, 34, 36, 38, 41, 43, 45, 47, 49, 50, 52, 54, 56, 58, 61, 63, 65, 67, 69, 70, 72, 74, 76, 78, 81, 83, 85, 87, 89, 90, 92, 94, 96, 98, 100, 101, 103, 104, 106, 107, 109, 110, 112, 113, 115, 116, 118, 119, 121, 122, 124, 125

Offset: 1

Reinhard Zumkeller, Aug 15 2010

Complement of A061383; A180160(a(n)) > 0;
A004426(a(n)) <> A004427(a(n)).
It seems 'obvious' that a(n) ~ n; is this true? - Charles R Greathouse IV, Feb 06 2013

R. Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A007953, A055642.

Select[Range[200],!IntegerQ[Mean[IntegerDigits[#]]]&]  (* Harvey P. Dale, Mar 27 2011 *)

is(n)=my(v=digits(n));sum(i=1,#v,v[i])%#v>0 \\ Charles R Greathouse IV, Feb 06 2013

A257295 Arithmetic mean of the digits of n, rounded to the nearest integer.

Original entry on oeis.org

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

Offset: 0

M. F. Hasler, May 10 2015

Coincides up to a(99) with the variant A004427 (= arithmetic mean of digits, rounded up). - M. F. Hasler, May 10 2015

0 <= a(n) <= 9. a(10*n + a(n)) = a(n). - Robert Israel, May 11 2015

Index entries for Colombian or self numbers and related sequences

Cf. A004426, A004427, A007953, A055642, A004428, A004429.

f:= proc(n) local L;
   L:= convert(n,base,10);
   round(convert(L,`+`)/nops(L))
end proc:
map(f, [$0..100]); # Robert Israel, May 11 2015

Round[Mean[IntegerDigits[#]]]&/@Range[0,110]

A257295(n)=round(sum(i=1, #n=digits(n), n[i])/#n) \\ ...Vecsmall(Str(n))...-48 is a little faster.

a(n)=round(sumdigits(n)/#digits(n)) \\ Charles R Greathouse IV, May 11 2015

a(n) = round(A007953(n)/A055642(n)).

A004426(n) <= a(n) <= A004427(n).

A074463 Average digit (rounded up) in the decimal expansion of a prime number p, where 2^p-1 is a Mersenne prime.

Original entry on oeis.org

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

Offset: 1

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

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

Cf. A000043, A004427, A074464.

f[n_] := Block[{id = IntegerDigits@ n}, Ceiling[Plus @@ id/Length@ id]]; lst = { (* terms from A000043 *) }; f@# & /@ lst (* Robert G. Wilson v, Jun 26 2013 *)
Ceiling[Mean[IntegerDigits[#]]]&/@MersennePrimeExponent[Range[47]] (* Harvey P. Dale, Feb 01 2023 *)

a(n) = A004427(A000043(n)). - Amiram Eldar, Oct 16 2024

a(43)-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.

cp's OEIS Frontend

A074462 Average digit (rounded up) in the decimal expansion of prime(n).

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A178404 Numbers such that the rounded up arithmetic mean of their digits equals their digital root.

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A178405 Numbers such that the rounded up arithmetic mean of their digits differs from their digital root.

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A180157 Arithmetic mean of digits is not an integer.

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A257295 Arithmetic mean of the digits of n, rounded to the nearest integer.

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A074463 Average digit (rounded up) 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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