A178405 -id:A178405 - cp's OEIS frontend

A004427 Arithmetic mean of digits of n (rounded up).

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, 1, 1, 1, 2, 2, 2, 3, 3

Offset: 0

N. J. A. Sloane

a(100)=1 is the first value that differs from the variant "... rounded to the nearest integer". - M. F. Hasler, May 10 2015

Cf. A178358, A178359, A178361, A178362, ..., A178369, A178401, A178402, A178403, A178404, A178405.

Cf. A000040, A004426, A007953, A055642, A061383, A074462.

Ceiling[Mean[IntegerDigits[#]]]&/@Range[0,110] (* Harvey P. Dale, Aug 29 2014 *)

A004427(n)=ceil(sum(i=1, #n=digits(n), n[i])/#n) \\ ...Vecsmall(Str(n))...-48 is a little faster. \\ M. F. Hasler, May 10 2015

From Reinhard Zumkeller, May 27 2010: (Start)
a(n) = ceiling(A007953(n)/A055642(n)); a(A000040(n)) = A074462(n);
A004426(n) <= a(n) with equality for n in A061383;
a(A178361(n)) = 1; a(A178362(n)) = 2; a(A178363(n)) = 3; a(A178364(n)) = 4; a(A178365(n)) = 5; a(A178366(n)) = 6; a(A178367(n)) = 7; a(A178368(n)) = 8; a(A178369(n)) = 9. (End)

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 *)

cp's OEIS Frontend

A004427 Arithmetic mean of digits of n (rounded up).

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